Answer
$\dfrac{131}{4}$
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:
$A=\int_a^b [f(x)-g(x)] \ dx\\ = \int_{-2}^{2} [12-4x-3x^2+x^3] \ dx +\int_{2}^{3} [3x^2-x^3-12+4x] \ dx \\= (12x-2x^2-x^3+\dfrac{x^4}{4}]_{-2}^2 +[x^3-\dfrac{x^4}{4}-12x+2x^2]_2^3 \ dx \\=12+20+(9-\dfrac{81}{4})-(-12) \\=\dfrac{131}{4}$
