Concept:Expand the product into a quadratic polynomial, then integrate term by term using the standard power rule.Explanation:First, expand the integrand: (x+1)(x−2)=x2−2x+x−2=x2−x−2.So the integral becomes −1∫0(x2−x−2)dx.Find the antiderivative: ∫(x2−x−2)dx=3x3−2x2−2x.Now evaluate from −1 to 0: [3x3−2x2−2x]−10.At x=0, the value is 0.At x=−1, the value is 3(−1)3−2(−1)2−2(−1)=−31−21+2=67.Therefore, the definite integral is 0−67=−67.Answer:−67, i.e. option D.