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$$ \frac{\mathrm d}{\mathrm dx}\left( \int_{a}^{b}{f\left(t\right)\mathrm dt} \right) $$

I understand if say $b=x$ then the answer will be $f(x)$. But what about this situation where a and b are only known to be constants?

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If $a$ and $b$ are both constants, than the integral will evaluate to a constant, so the derivative with respect to x would just be $0$.