Cálculo de integrales definidas

ENUNCIADO. Calcúlese la integral definida $$\displaystyle \int_{-2}^{2}\,f(x)\,dx$$ donde $$f(x)=\left\{\begin{matrix}x^2+1 & \text{si} & x \prec 0 \\ -x+3 & \text{si} & x \ge 0\end{matrix}\right.$$

SOLUCIÓN.
$\displaystyle \int_{-2}^{2}\,f(x)\,dx=\int_{-2}^{0}\,(x^2+1)\,dx+\int_{0}^{2}\,(-x+3)\,dx=$
    $=\left[\dfrac{1}{3}\,x^3+x\right]_{-2}^{0}+\left[-\dfrac{1}{2}\,x^2+3x\right]_{0}^{2}=$
        $=\left(\dfrac{1}{3}\,0^3+0\right)-\left(\dfrac{1}{3}\,(-2)^3+(-2)\right)+\left(-\dfrac{1}{2}\,2^2+3\cdot 2\right)-\left(-\dfrac{1}{2}\,0^2+3\cdot 0\right)=\dfrac{26}{3}$
$\square$