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Riemann integration

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Which of the following conditions are necessary for a function f to be Riemann integrable on the closed interval [a,b], where a < b?
I. f is bounded on [a,b].
II. f is continuous on [a,b].
III. f is differentiable on [a,b].

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This discusses the requirements for Riemann integrability.

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The answer is A. None of them are necessary.
I. f is bounded on [a,b].
This is not necessary. Here is an example. f(x)=1/sqrt(|x|) on the ...

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