One definition of in·teg·ri·ty is the quality of being honest and having strong moral principles; moral uprightness. Our society has lost much of this, though not all, because many do not personalize integrity.
per·son·al in·teg·ri·ty for me is to do the right thing, after review of facts and circumstance, even when it does not benefit you, or may well cause you harm.
I am not suggesting that this be taken to bodily harm, it could be a simple as an inconvenience or a bearable financial cost. There can be many possible payoffs though none guaranteed. What has value depends on you and may not be evident to others. You may simply find yourself stronger internally and standing taller in view of the world without anyone knowing.