Integrity rhymes with:
alacrity, authority, barbarity, celerity, clarity, dexterity, disparity, dissimilarity, familiarity, geraghty, hanratty, hilarity, impurity, irregularity, majority, maturity, mcgarity, mcgarrity, mediocrity, minority, moriarity, obscurity, parity, particularity, peculiarity, polarity, popularity, posterity, priority, prosperity, purity, rarity, regularity, security, similarity, sincerity, solidarity, sorority, surety, temerity, unfamiliarity, verity
Integrity sounds like:
indiscreet, integrate, integrated