已知 $f(x)=\max \left\{1, x^2\right\}$, 则 $\int f(x) d x=$
A
$\begin{cases}\frac{x^3}{3}-\frac{2}{3}+C, & x < -1 \\ x+C, & -1 \leq x \leq 1 \\ \frac{x^3}{3}+\frac{2}{3}+C, & x>1\end{cases}$
B
$\left\{\begin{array}{cc}\frac{x^3}{3}+C, & x < -1 \\ x+C, & -1 \leq x \leq 1 \\ \frac{x^3}{3}+C, & x>1\end{array}\right.$
C
$\left\{\begin{array}{cc}\frac{x^3}{3}+C_1, & x < -1 \\ x+C_2, & -1 \leq x \leq 1 \\ \frac{x^3}{3}+C_3, & x>1\end{array}\right.$
D
$\left\{\begin{array}{l}\frac{x^3}{3}-\frac{4}{3}+C, \quad x < -1 \\ x+C, \quad-1 \leq x \leq 1 \\ \frac{x^3}{3}+\frac{2}{3}+C, \quad x>1\end{array}\right.$
E
F