By definition, integrity is the state of being whole, entire or undiminished. Basically, it means to be honest, to be real. How often do people mean what they say and say what they mean?
Whether you say you're fine, and you're not; you say you'll be there at 9am and you're not (you flake out or you're late); you make a promise and you break it. We often rationalize the reasons for bailing on someone or something (any New Year's Resolutions come to mind?) or not holding true to our word.
But here's the thing: every time you rationalize these scenarios, you weaken your character, your state of being whole, entire and undiminished and instead.
If you are told a secret, keep it. If you say something, mean it. If you commit to it, stick to it (through the light and the dark). If you say YES, let it in - no matter how hard. If you offer your assistance, mean it with every single, savvy cell of your being. If you say now, be ready for it.