= Solution
The <fundamental theorem of calculus> states that integrating a continuous <function> from a fixed lower endpoint produces an <antiderivative>. More precisely, if $f$ is continuous at the interior point $x$, then
$$
\boxed{\frac{d}{dx}\int_a^x f(y)\,dy=f(x)}.
$$
Indeed, the difference quotient is the average of $f$ over the short interval from $x$ to $x+h$, which tends to $f(x)$ by <continuity>. The accompanying evaluation rule is $\int_a^b f=F(b)-F(a)$ whenever $F'=f$ on the interval.
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