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                            October 6, 2021

       Enrique Klix
       Chief Executive Officer
       Integral Acquisition Corporation 1
       667 Madison Avenue
       New York, New York 10065

                                                        Re: Integral
Acquisition Corporation 1
                                                            Amendment No. 2 to
Registration Statement on Form S-1
                                                            Filed September 24,
2021
                                                            File No. 333-257058

       Dear Mr. Klix:

             We have reviewed your amended registration statement and have the
following
       comments. In some of our comments, we may ask you to provide us with
information so we
       may better understand your disclosure.

              Please respond to this letter by amending your registration
statement and providing the
       requested information. If you do not believe our comments apply to your
facts and
       circumstances or do not believe an amendment is appropriate, please tell
us why in your
       response.

              After reviewing any amendment to your registration statement and
the information you
       provide in response to these comments, we may have additional comments.

       Amendment No. 2 to Form S-1 filed September 24, 2021

       The Offering
       Founder Shares Conversion and Anti-Dilution Rights, page 19

   1.                                                   We note your disclosure
that the founder shares will automatically convert into 20% of the
                                                        total number of shares
of Class A common stock outstanding after the conversion,
                                                        including the total
number of Class A shares of common stock issued, or deemed to be
                                                        issued or issuable upon
conversion or exercise of any equity-linked securities or rights
                                                        issued or deemed issued
by the Company in connection with or in relation to the
                                                        consummation of the
initial business combination, including the forward purchase shares.
                                                        Please tell us how you
assessed the founder shares under ASC 815. Additionally,
 Enrique Klix
Integral Acquisition Corporation 1
October 6, 2021
Page 2
      irrespective of any other conclusion under ASC 815, please tell us how
you evaluated
      whether this feature on its own would meet the criteria in ASC 815-40-15
for equity
      classification.
Notes to Financial Statements
Note 7 Stockholders' Equity, page F-17

2.    We note that section 6.5 of the warrant agreement states that the private
placement
      warrants or working capital warrants that are transferred to persons
other than permitted
      transferees cease to be private placement warrants or working capital
warrants and shall
      become public warrants under the agreement. Tell us how you considered
the cashless
      exercise provisions discussed in section 2.6 and 3.3 of the warrant
agreement and explain
      whether you believe there are potential changes to the settlement amounts
that are
      dependent upon the characteristics of the holder of the warrant. If so,
tell us how you
      concluded that such a provision would not preclude the warrants from
being indexed to
      the entity   s stock based on the guidance in ASC 815-40.
       You may contact Franklin Wyman at 202-551-3660 or Daniel Gordon at
202-551-3486 if
you have questions regarding comments on the financial statements and related
matters. Please
contact Jane Park at 202-551-7439 or Irene Paik at 202-551-6553 with any other
questions.



                                                           Sincerely,
FirstName LastNameEnrique Klix
                                                           Division of
Corporation Finance
Comapany NameIntegral Acquisition Corporation 1
                                                           Office of Life
Sciences
October 6, 2021 Page 2
cc:       Barry Grossman, Esq.
FirstName LastName