There's a theorem in my real analysis textbook that says(adsbygoogle = window.adsbygoogle || []).push({});

A function f is Riemann-integrable iff the set of its points of discontinuity is of measure zero.

But take say f(x)=1/x. It is only discontinuous as x=0, but it's not integrable on (-e,e). :grumpy:

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# Lebesgue's criterion

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