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If $f(x)$ is derivable,and $f'(x)$ is Riemann integrable, the continuity point of $f'(x)$ is dense, i.e. the measure of the set of discontinuity point of the second kind is zero. I'm thinking out that is it true that for all the derivable functions, $f'(x)$ is Riemann integrable? If not,can anyone give me a counterexample?

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    A function can have more than one discontinuity point (and needs not have any). Do you mean "the measure of the _set of discontinuity points_"?2012-04-23
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    @HenningMakholm Sorry,I make a mistake.2012-04-23

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