I was reading Psalms 15, I noticed it speaks of a man who walks in integrity, and he "changes not his mind." Does that mean it is wrong to change plans or reschedule on a friend or to change one's mind about doing something? Like my friend and I were supposed to go to the gym (told him I could go the day before), but then I got invited to go skating with some friends, and I did that instead. I told him that I was going skating, and we could reschedule for gym the following day. He was understanding. Is that wrong or does that lack integrity?
The Hebrew word, tom, is translated as "integrity" in many versions. It means "innocent of willful wrongdoing." Thus, when Abimelech declared his innocence regarding his taking Abraham's wife, Sarah, he was saying that he did not purposely set out to steal another man's wife (Genesis 20:5). When Absalom overthrew David, a number of men were caught up in his plot, but they were innocent of rebellion against the true king (II Samuel 15:11).
"O LORD, who may abide in Your tent? Who may dwell on Your holy hill? He who walks with integrity, and works righteousness, and speaks truth in his heart. He does not slander with his tongue, nor does evil to his neighbor, nor takes up a reproach against his friend; in whose eyes a reprobate is despised, but who honors those who fear the LORD; he swears to his own hurt and does not change; he does not put out his money at interest, nor does he take a bribe against the innocent. He who does these things will never be shaken" (Psalms 15).
So does having integrity mean you never changing your mind? God is always the ultimate example of righteousness; yet, there are times when He changed His mind. In response to the evil of men in the days of Noah, "Then the LORD saw that the wickedness of man was great in the earth, and that every intent of the thoughts of his heart was only evil continually. And the LORD was sorry that He had made man on the earth, and He was grieved in His heart" (Genesis 6:5-6). God had not changed His nature -- man changed -- and in response to man's change, God changed how He dealt with men.
Paul changed his plans regarding his visit to Corinth. See: Changed Plans for a detailed discussion.
You changed your plans because circumstances changed. You still went to the gym with your friend, just on a different day than what you originally intended.
What Psalms 15 discusses is keeping a promise that another person is relying upon, such as a business transaction, even when keeping it may cost you more money. It is not discussing situations where things are out of your control, but ones where you could have done something about it, but willfully didn't to save yourself costs. Such is a lack of integrity.