Having integrity means not putting on an act. If you're trying too hard to please rather than be yourself, that comes across as dishonest and untrustworthy.
I don't really want to put on an act, I guess I'm asking for more "how do you present forward the more positive parts of your personality and quiet the bad parts during an interview?"
I acknowledge there is still some dishonesty in that, my personality is a package deal, good and bad, but I do think that most of my coworkers end up liking me after they get to know me.