Last Friday, November 2, 2007 Chuck Swindoll on his radio program, Insight For Living, gave a sermon called Enjoying the Rewards. He talked about integrity. He gave several references. One was about David when he was young and God chose him to be the next king of Israel.
Psalm 78:70-72 (King James Version)
He chose David also his servant,
and took him from the sheepfolds:
From following the ewes great with young he brought him to feed Jacob his people,
and Israel his inheritance.
So he fed them according to the integrity of his heart;
and guided them by the skilfulness of his hands.
–Even when David was young he was developing leadership skills. He was strong in integrity and honesty.
King David was a man of integrity and he taught his young son such things and his son, Solomon wrote many of the Proverbs:

Proverbs 10:9
He that walketh uprightly walketh surely:
but he that perverteth his ways shall be known.
(This is a contrasting Proverb.)
Proverbs 11:3
The integrity of the upright shall guide them:
but the perverseness of transgressors shall destroy them.
Proverbs 13:6
Righteousness keepeth him that is upright in the way:
but wickedness overthroweth the sinner.
Proverbs 20:6-7
Most men will proclaim every one his own goodness:
but a faithful man who can find?
The just man walketh in his integrity:
his children are blessed after him.
(This is a favorite of Dr. Swindoll from the Proverbs)
Proverbs 28:6
Better is the poor that walketh in his uprightness,
than he that is perverse in his ways, though he be rich.