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## Main Question or Discussion Point

Hi guys

I have been wondering: Say we have a continuous function

Now, the problem is that I cannot deduce continuity of

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?

I have been wondering: Say we have a continuous function

*f*. I integrate*f*to obtain its anti-derivative called capital*f*, i.e.*F*. Now I wish to prove the differentiability of*F*, and in order to do so, I need the fact that*F*is continuous (this is just something I need in my proof).Now, the problem is that I cannot deduce continuity of

*F*on the fact that*F*is differentiable, since I wish to prove the differentiability of*F*. 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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