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I have this function $f(x)$ which is continuous and differentiable on $\mathbb R$. Is the following true - without the assumption that $f$ being absolutely continuous!

$$ \int_{a}^{b} f'(x) dx=f(b)-f(a)$$

Edit: $f$ is infinitely differentiable on $\mathbb R$. I think this may change everything!

2 Answers 2