Integrity (from "integer" = the whole of anything, a whole number not a fraction - think "whole character" not a fraction of one!) speaks of the unimpaired state of one's mind and heart, of moral soundness and purity, of incorruptness, of uprightness, of honesty. Just as we would talk about a whole number, so also we can talk about a whole person who is undivided. A person of integrity is living rightly, not divided, nor being a different person in different circumstances. A person of integrity is the same person in private that he or she is in public.
Integrity is derived from "integer" (a whole number as opposed to a fraction) and speaks of the quality of being undivided. O, to be men and women of integrity, lights shining in the midst of the darkness in such a way that the world might see our undivided hearts and this would bring glory to our Father Who is in heaven. (Mt 5:16-note, cf Php 2:15-note).
A great prayer to pray (daily) would be David's words...
ARE YOU ENTANGLED? - In some of his last words to Timothy, Paul wrote that "No soldier in active service ENTANGLES himself in the affairs of everyday life ("civilian pursuits"), so that he may please the One Who enlisted him as a soldier." (2Ti 2:4-note)