If a function has an antiderivative, is it always integrable?

Question

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.

score 2 · Accepted Answer · answered Feb 18 '16 at 05:17

2

No, this is not necessary; a counterexample is the derivative of Volterra's function.

answered Feb 18 '16 at 05:17

detnvvp

1 Answers1