Answer
$f(4)=29$
Work Step by Step
To answer this question, we must use the fundamental theorem of Calculus. We are given that $f(1)=12$, $f'(x)$ is continuous, and that $\int_{1}^{4} f'(x) dx = 17$.
$$\int_{1}^{4} f'(x) dx = f(4) - f(1)$$
All we need to do to solve is plug in what we know.
$\int_{1}^{4} f'(x) dx = 17$ & $f(1)=12$
$17 = f(4) - 12$
Therefore,
$f(4) = 29$
