Integrity involves honesty and truthfulness, but the concept of integrity is much broader than this.  "Integrity" comes from a root word that means "whole," or "intact," or "complete."  Integrity means that what a person believes, and says, and does all come together in a whole.  Ananias and Sapphira weren't people of integrity; and the truth is, it's possible for us to be like Ananias and Sapphira, maybe more than we would like to admit.  But God is always full of grace.