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    I'm pretty sure the claim isn't true: consider the integral from x = -1 to x = 1 of 1/(x^2 - 1) which does not converge...

    Are you sure you've given all necessary info? Do you need to show it's Riemann integrable over [a,b] or (a,b)?

    Thanks,
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    Ah I see. It isn't true for general f but it may be for your case, depending on the singularities...

    The proof using Reimann's condition will rely on the behaviour of the function (you need to general a series of values of f(x_i), with equally spaced points x_i, such that the sum of the points f(x_i) is arbitrarily close to a finite value).

    Can you provide the function f? This is really the only way to explain. In general terms, you will need to define some value e>0, then find d such that if the x_i are spaced d apart, the sum of f(x_i) over i is within e of a number. The key thing is to determine the variable d and the number you need to be close to.

    Thanks,
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Updated: January 20, 2015
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