I see integrity as being the same person around everyone. Kipling talks about keeping your virtue in a crowd and not losing the common touch while walking with kings. Few of us live up to that. For example, I curse around some people, but around others I wouldn’t dare. It would show more integrity to curse around everyone than to split who I am into separate parts. Better still would be not to do it at all.
Whatever you do, be authentic, show some integrity, don’t be ashamed of who you really are. Let the world appreciate the real you as much as your closest friends and the people you look up to most do.