Chọn phương án D.

Phương trình hoành độ giao điểm: $$\begin{aligned}x^2+x=-x+3\Leftrightarrow&x^2+2x-3=0\\
\Leftrightarrow&\left[\begin{array}{l}x=-3\\x=1\end{array}\right.\end{aligned}$$

Khi đó $$\begin{aligned}
S&=\displaystyle\int\limits_{-3}^1\left|x^2+x-(-x+3)\right|\mathrm{\,d}x\\
&=\displaystyle\int\limits_{-3}^1\left|x^2+2x-3\right|\mathrm{\,d}x\\
&=-\displaystyle\int\limits_{-3}^1\left(x^2+2x-3\right)\mathrm{\,d}x\\
&=-\left(\dfrac{x^3}{3}+x^2-3x\right)\bigg|_{-3}^1\\
&=\dfrac{32}{3}.
\end{aligned}$$