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An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$.

I have to show if $f\in \mathcal L[-\pi,\pi]$ and if $$f(u+2\pi)=f(u), (-\infty

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    This is basically the same question as: [An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$.](http://math.stackexchange.com/questions/94233/an-integrable-and-periodic-function-fx-satisfies-int-0tfxdx-int)2012-06-03
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    I don't know that this question already asked! Sorry for that! But you can tell me am i justify the answer of this question?2012-06-03

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It looks correct and pretty nice, indeed.