If it’s true that integrity is what you exhibit when nobody’s looking, it’s also true (by implication) that integrity is something you do for your OWN sake. This means that morality, which integrity serves, ought to be self-interested and rational — not stupid, enabling of others’ wrong behaviors or sacrificial to one’s own well-being, as we’re typically taught. Morality is for the advancement of your own life. You display integrity for your own benefit. Don’t worry about the benefit of others, as they’ll do just fine if they subscribe to the same principle.