Answer
$\dfrac{125}{6}$
Work Step by Step
Let us consider that two continuous functions $f(x)$ and $g(x)$ with $f(x)\geq g(x)$ on the interval $[a,b]$ . The area (A) of the region bounded by the graph of $f(x)$ and $g(x)$ on the interval $[a,b]$ can be calculated as: $Area(A)=\int_a^b [f(x)-g(x)] \ dx$
Thus, the area of the region is:
$A=\int_a^b [f(x)-g(x)] \ dx= \int_{-3}^{2} [2x-(x^2+3x-6)] \ dx\\=\int_{-3}^{2} [-x^2-x+6] \ dx \\=|\dfrac{-x^3}{3}-\dfrac{x^2}{2}+6x|_{-3}^2\\=\dfrac{125}{6}$