Is to do what we say and say what we feel. 

The etymology means to be one or to be whole. 

The opposite, then is duality.

Where we don't do what we say or don't say what we feel.

Leading to beliefs and opinions that we hold in our heads, that varies from what we share with others as our opinions and beliefs.

And the stronger the differences in this duality, the more difficult it is to stay sane and hold the two positions - one private in our head and one public we share with others.

Integrity, first and foremost, is a tool for us to resolve the conflicts in our behaviour as perceived by others.