[m]S=\int_{0} ^{\frac{\pi}{2}}sinxdx=(-cosx)|_{0} ^{\frac{\pi}{2}}=-(cos\frac{\pi}{2}-cos0)=-(0-1)=1[/m]
[m] S=\int_{0} ^{1}(1-x^3)dx=(x-\frac{x^4}{4})|_{0} ^{1}=1-\frac{1}{4}=\frac{3}{4}[/m]
[m] S=\int_{-1} ^{0}(-x^2-2x+2)dx=(-\frac{x^3}{3}-2\frac{x^2}{2}+2x)|_{0} ^{-1}=0-(\frac{1}{3}-1-2)=\frac{8}{3}[/m]