[m]S= ∫ ^{2}_{-1}(x-1-(x^2-3))dx= ∫ ^{2}_{-1}(x-x^2+2)dx=(\frac{x^2}{2}-\frac{x^3}{3}+2x)|^{2}_{-1}=\frac{2^2}{2}-\frac{2^3}{3}+2\cdot 2)-(\frac{(-1)^2}{2}-\frac{(-1)^3}{3}+2\cdot (-1))=[/m]
[m]=\frac{10}{3}-(-\frac{7}{6})=\frac{27}{6}=\frac{9}{2}[/m]