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I have been wondering: Say we have a continuous functionf. I integratefto obtain its anti-derivative called capitalf, i.e.F. Now I wish to prove the differentiability ofF, and in order to do so, I need the fact thatFis continuous (this is just something I need in my proof).

Now, the problem is that I cannot deduce continuity ofFon the fact thatFis differentiable, since I wish to prove the differentiability ofF. What can I do instead?

I thought of using the argument (which I am not sure is correct) that the integral of a continuous function is continuous. Am I allowed to do this?

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# Is the anti-derivative of a continuous function continuous?

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