I've taken differential and integral calculus, and have a fair understanding of the material at this point. Last semester I had a professor show something in class that I feel is a pretty basic idea, I just haven't thought about working things in such a way. He put a derivative on the board such as the one for instantaneous current in a circuit. He went on to say "you may have not seen this before or knew that you are allowed to do this" and rearranged the formula to then integrate both sides and end up with a new equation. It is this method I'm interested in. I wonder if there is any material out there that explains this way of rearranging a derivative for example and coming up with new equations by integrating both sides, it's a newish idea to me and want to read more about how or why that works, the motive of it. I haven't had much luck searching for any literature on it, maybe I don't know how to phrase the search term well enough.