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one often reads

[itex]\int_A f(x) dx = \int_A g(x) dx [/itex] for arbirary A, thus f(x) = g(x), since the equaltiy of the Integrals holds for any domain A.

I don't see, why the argument "...for any domain A..." really justifies this conclusion.

Can someone explain this to me, please?

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# Equality of integrals => equality of integrands

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