Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises - Page 321: 57

$\frac{-20}{3}$

We can calculate the area by integrating the function from -3 to 2. $\int_{-3}^{2} (-x^2-2x)dx =[\frac{-x^3}{3}-x^2]_{-3}^{2}=[\frac{-2^3}{3}-2^2]-[\frac{-(-3)^3}{3}-(-3)^2]=[\frac{-8}{3}-4]-[\frac{27}{3}-9]=[\frac{-20}{3}]-0=\frac{-20}{3}$