TITLE: If a function has an antiderivative, is it always integrable?
QUESTION [5 upvotes]: If a function $f$ defined on $[a,b]$ has an antiderivative on $[a,b]$, is it always Riemann integrable?  I can't think of a counterexample.

REPLY [2 votes]: No, this is not necessary; a counterexample is the derivative of Volterra's function.