When I was a student of physics and came across this paragraph in Feynman's book, I was curious if he really meant the simple technique explained in the article, a more general one (also described in the article with the integral bounds as functions of a parameter) or something else. I don't know, but this led me to read the text "Advanced Calculus" by Edwin Bidwell Wilson (1912), which includes a lot of examples and gems. If there is some young student out there who wants to go well beyond the basic techniques of calculus taught in analysis or mathematical physics courses, have a look at [0].

[0] https://archive.org/details/advancedcalculus031579mbp/mode/1...