<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-11-02</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001850262</issuerCik>
        <issuerName>Integral Acquisition Corp 1</issuerName>
        <issuerTradingSymbol>INTEU</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001891766</rptOwnerCik>
            <rptOwnerName>Thornton Lynne</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>INTEGRAL ACQUISITION CORPORATION 1</rptOwnerStreet1>
            <rptOwnerStreet2>667 MADISON AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10065</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>The reporting person does not beneficially own any securities. The reporting person has an indirect pecuniary interest in shares of common stock of the registrant through his membership interest in Integral Sponsor LLC, over which the reporting person does not have voting or dispositive control.</remarks>

    <ownerSignature>
        <signatureName>/s/ Lynne Thornton</signatureName>
        <signatureDate>2021-11-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
