From several dictionaries, I found out that honesty means a lot of things: trustworthiness, virtue, chastity, good rapport, integrity, uprightness, morality, honor and fairness.
As I think of that, I recall what Joseph Smith wrote in the 13th article of faith:"We believe in being honest, true, chaste, benevolent, virtuous, and in doing good to all men; indeed, we may say that we follow the admonition of Paul - We believe all things, we hope all things, we have endured many things, and hope to be able to endure all things. If there is anything virtuous, lovely, or of good report or praiseworthy, we seek after these things."
To have integrity then, we must be honest and righteous.
Alma described some people of integrity and honesty in his time:
"And they were among the people of Nephi, and also numbered among the people who were of the church of God. And they were also distinguished for their zeal towards God, and also towards men; for they were perfectly honest and upright in all things; and they were firm in the faith of Christ even unto the end." (Alma 27:27.)
I have to smile at true-life situations, but who hasn't found it difficult to be totally honest at times?
When I was a boy of 11 years old I could never tell a lie or fib or be dishonest without being found out. My brother and I used to go to a farm and pinch turnips and eat them in the barn until the farmer caught us. Of course, like boys, we ran. I stood outside my house looking over the field and felt the biggest hand clamp my shoulder. It was the farmer. He asked me two questions: what was my name and where did I live. I told him my name but said I couldn't remember where I lived. As he was about to leave and let me go, I saw my dad approaching, and then I told the farmer to ask my dad where I lived. My dad and he looked at each other and smiled. I could never get away with anything. I got punished later on for not being honest.
Another incident comes to mind. When I was interviewing a member for a temple recommend, I asked him all the questions. We started to talk, and I felt something was wrong, but he insisted everything was all right. So I signed the temple recommend, and he left my office. Five minutes had elapsed, and I knew the man was not telling the truth, so I went to get him. As I opened the door, he was right outside. He said, "Bishop, I have lied."
We threw our arms around each other, and he told me that he smoked. He was overwhelmed with relief that he told the truth. He became closer to his wife, family and the Church, and most of all, he could face his children. He stopped smoking. Now this brother's whole family is sealed to him.
It is through this saving grace of honesty that we conform to all the divine standards with which Latter-day Saints must comply.