Given: $f(x)=x^3+5x^2-2x-23$ and $g(x)=-x^3-5x^2+2x+25,$

the area of the region bounded by the graphs of $f(x)$ and $g(x)$ is given by

$($Choose all the correct answers below$)$

The described region is unbounded and hence the area cannot be calculated.

Area $={\displaystyle \underset{2}{\overset{-3}{}}}[f(x)-g(x)]dx+{\displaystyle \underset{-3}{\overset{-4}{}}}[g(x)-f(x)]dx$

Area $={\displaystyle \underset{-4}{\overset{-3}{}}}[f(x)-g(x)]dx+{\displaystyle \underset{-3}{\overset{0}{}}}[g(x)-f(x)]dx+{\displaystyle \underset{0}{\overset{2}{}}}[g(x)-f(x)]dx$

$($D$)$ Area $={\displaystyle \underset{-4}{\overset{-3}{}}}[f(x)-g(x)]dx+{\displaystyle \underset{-3}{\overset{2}{}}}[g(x)-f(x)]dx$

Area $=\frac{344}{3}$

Area $=\frac{443}{3}$

$($G$)$ Area $={\displaystyle \underset{-4}{\overset{-2}{}}}[f(x)-g(x)]dx+{\displaystyle \underset{-2}{\overset{2}{}}}[g(x)-f(x)]dx$