Regarding your last sentence, I'm thinking back to my differential geometry course, and I'm not even sure if we ever calculated an integral that wasn't equal to

Regarding your last sentence, I'm thinking back to my differential geometry course, and I'm not even sure if we ever calculated an integral that wasn't equal to 0. Totally agree with the rest of the sentence though: I don't think I quite got it right away, but I felt better off for the experience.