Question 2 (1 point)
3
The table below gives the value of a function $f$ and its derivative $f^{\prime}$ at several values of $x$.
6
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline$x$ & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline$f(x)$ & 6 & -1 & 1 & 5 & -6 & 3 \\
\hline$f^{\prime}(x)$ & -2 & -2 & 0 & 4 & 5 & 1 \\
\hline
\end{tabular}
9
Use the table to compute $\int_{4}^{2} f^{\prime}(x) d x$.
5
$-5$
1
4
7

Step 1 ：The table below gives the value of a function $f$ and its derivative $f^{\prime}$ at several values of $x$.\n\n\begin{tabular}{|c|c|c|c|c|c|c|}\n\hline$x$ & 0 & 1 & 2 & 3 & 4 & 5 \\\n\hline$f(x)$ & 6 & -1 & 1 & 5 & -6 & 3 \\\n\hline$f^{\prime}(x)$ & -2 & -2 & 0 & 4 & 5 & 1 \\\n\hline\n\end{tabular}

Step 2 ：Use the table to compute $\int_{4}^{2} f^{\prime}(x) d x$.

Step 3 ：The integral of a function's derivative from a to b is equal to the function's value at b minus the function's value at a. This is a direct application of the Fundamental Theorem of Calculus. In this case, we are asked to compute $\int_{4}^{2} f^{\prime}(x) d x$, which is equal to $f(2) - f(4)$. We can find these values from the given table.

Step 4 ：From the table, we find that $f(2) = 1$ and $f(4) = -6$.

Step 5 ：Subtracting these values, we find that $\int_{4}^{2} f^{\prime}(x) d x = f(2) - f(4) = 1 - (-6) = 7$.

Step 6 ：Final Answer: The value of $\int_{4}^{2} f^{\prime}(x) d x$ is $\boxed{7}$.