$[15$pts$.]$ Find the area bound by the given curves. First find the intersections and then determine which is $f(x)$ and $g(x).$ Either sketch or use the $x-$value to check which one has the greater $y-$value. Find the antiderivative then apply the Fundamental Theorem of Calculus to receive full credit: $y=2+x-2x^2$ and $y=3x^2-2.$