Yeah, that brings up another of those peculiar things about math, and especially, dealing with math culture. It's hard to talk about a main idea without gettin

Yeah, that brings up another of those peculiar things about math, and especially, dealing with math culture. It's hard to talk about a main idea without getting mired in weird exceptions. There are indeed precise conditions that guarantee that a function can (a) be integrated and (b) the integral can be differentiated, and there are subtly different definitions of "integral" that lead to different sets of extremely weird functions being integrable or not. I can't remember any of the details despite having come across them many times. In software culture, it seems much easier to talk in broad strokes when appropriate and in precise details when appropriate. You might get an argument, but it's usually about something relevant.