<?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>0001891772</rptOwnerCik>
            <rptOwnerName>Lincoln Brittany</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>The reporting person does not beneficially own any securities.</remarks>

    <ownerSignature>
        <signatureName>/s/ Brittany Lincoln</signatureName>
        <signatureDate>2021-11-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
