Answer
$$F(x) =2x^2+7x+C$$
Work Step by Step
Given $$f(x) =4x+7=4x^{1}+7$$
Then by using if $f(x)=x^{\alpha}\ \to\ \ F(x) = \frac{x^{\alpha+1}}{\alpha+1}+C$
\begin{align*}
F(x) &=\frac{4x^2}{2}+\frac{7x^{0+1}}{1}+C\\
&=2x^2+7x+C
\end{align*}
To check
\begin{align*}
F'(x) &=4x+7\\
&=f(x)
\end{align*}
