Answer
$g'(x) = \frac{d}{dx}\left[\int_a^x f(t)\,dt\right] = f(x)$.
Explanation
Differentiation and integration are inverse operations. Furthermore, $\int_a^b f(x)\,dx = F(b) - F(a)$ where $F'(x) = f(x)$.
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What is the Fundamental Theorem of Calculus, Part 1, for $g(x) = \int_a^x f(t)\,dt$ where $f$ is continuous?
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