Expanding (x+1)(x−2)=x2−2x+x−2=x2−x−2
0∫−1(x2−x−2)dx=[x33−x22−2x]−10
= [03−02−2×0−(−133−−122−2×−1)]
= 0+13+12−2=−76
Note: This can also be solved using integration by parts.
∫uvdx=u∫vdx−∫u′(∫vdx)dx.