I lived with a buddy who was always so intense about everything around the house. No one did the dishes, someone drank his beer so we ended up calling him Captian intensity
The act of pretending to be an honest, trustworthy, and overall great person of high moral values; but they really don't follow through with anything and in turn have no real friends. Sometimes this person may have a breakthrough about how fake their life is, and may change their ways, but years of of deceit and blaming everyone else causes this person to repeat their old behavior. They will break your heart.
Guy: Dude, I know she's had her ups and downs but she says she loves me and wants to have my kids!
Best friend: Listen homey, I've heard it all before. She's called the cops on you when she was drunk. She comes stumbling home drunk as hell, blacks out, kicks you out of the house, and calls you in the morning apologizing and begging you to come back. Fuck man, this bitch flaked on you at the music festival cause she was so trashed and leaves you with her one year old baby because she forgot about her! She don't love you man. She changes every day with false hopes of creating a future with you but she's full of untegrity. Now let's get drunk because you're trippin and she's full of untegrity!
Don't listen to the guy above talking about integration. Integration is NOT the reversal of differentiation. That would be the anti-derivative. Integrals and anti-derivatives are NOT the same thing. But they are connected by the Fundamental Theorem of Calculus.
If a function f(x) has an anti-derivative F(x), the area under the curve from a to b is equal to F(b)-F(a).