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Lets say that f(x) is continuous. Then [itex] \int_0^x \! f(t)dt=G(x)[/itex] is continuous. (I don't think you have to say that f need to be continuous for this, all we need to say is that f is integrable?, or do we need continuity of f here?)

But my main question is about the converse. lets say that [itex] \int_0^x \! f(t)dt=G(x)[/itex] is continuous, does that imply that f is continuous?

Have a nice sunday.

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# Continuity of one function, implies continuity of another?

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