What's the verb for integrity? Here's the word you're looking for.
integrate
To form into one whole; to make entire; to complete; to renew; to restore; to perfect.
To include as a constituent part or functionality.
To indicate the whole of; to give the sum or total of; as, an integrating anemometer, one that indicates or registers the entire action of the wind in a given time.
(mathematics) To subject to the operation of integration; to find the integral of.