Answer
$$29$$
Work Step by Step
Given
$$\int_{1}^{4} f^{\prime}(x) d x=17,\ \ \ f(1)= 12$$
By using the Fundamental Theorem of Calculus (2)
\begin{aligned}
\int_{1}^{4} f^{\prime}(x) d x&=f(4)-f(1)\\
17&= f(4)-12
\end{aligned}
Then
\begin{aligned}
f(4)&= 17+12\\
&=29
\end{aligned}