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Is there a function f such that?

$$\int_{0}^x f(t) dt=x+1 $$

I used the FTC but i don't now where the +1 coming from ?

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    Think about what happens when $x=0$. – 2017-02-15

1 Answers 1

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It sounds as though you answered your own question.

Suppose that such a function did exist. Then applying the FTC gives $$f(x) = 1$$ but then $$\int_{0}^{x}f(t)dt = x\neq x+1$$ so you have reached a contradiction, and no such function exists.

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    It's OK, but doesn't the FTC give $f(x)=1$ *almost everywhere*? – 2017-02-15