Can F'(x) =f(x) even if f is not continuous(adsbygoogle = window.adsbygoogle || []).push({});

I tried making a function let

f(x) =5 if x<=5

f(x)=4 if x>5

f is not continuous at 5

Then F(x) =5x x<=5

F(x) =4x+5 x>5

Clearly F is continuous at 5 but F is not differentiable at 5..

So is there a discontinuous function that has F'(x) =f(x) for every x?

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# Does a discontinuous function for have an antiderivative?

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