Regarding the First Fundamental Thereom of Calculus why does the theorem (or at least the way it is given in the book Advanced Calculus by Fitzpatrick) only take into account continuous derivatives? Derivatives can never have jump/removable discontinuities by Darboux’s Theorem, but they can have essential discontinuities, which would mean an antiderivative would exist. Is it maybe because derivatives with essential discontinuities may have boundedness issues and thus, not be Riemann integrable - so no point in taking them into account?
2026-05-16 09:05:21.1778922321
First Fundamental Thm of Calculus Question
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