Integrity is often used to describe people and their traits. Merriam-Webster defines integrity as the adherence to a code, the quality of being honest and fair, and as the state of being complete or whole. The origin of the word integrity comes from the Latin word “integer,” which means whole or complete. Some synonyms include decency, goodness, honesty, morality, rightness, and virtue. Some descriptions of integrity are exhibiting conduct that conforms to accepted standards of right and wrong, remaining truthful even when it means taking responsibility for failures, and being faithful to high moral standards.
A prerequisite to integrity is to have established norms, standards, behaviors, etc., that everyone agrees are generally appropriate and applicable to all situations. You have to have basic principles that are universally agreed to, that form the foundation for what determines right vs wrong. Some typical examples of traits generally recognized as describing people with integrity are truthful, fair, consistent, disciplined, etc.