Given the functions $f(x)=x^2-3x+2$ and $g(x)=30-6x,$ write the integral to find the area of the region pictured below that is bounded above by $f(x)$ and $g(x)$ and bounded below by the $x-$axis when integrating with respect to $y.$ Do not evaluate the integral.

$R$ is the region bounded by the functions $f(x)=3x^2+27x+54$ and $g(x)=-\frac{3x^2}{2}-\frac{27x}{2}-27.$ Find the area $A$ of $R.$ It can be helpful to graph the functions to better determine the correct region.

Enter an exact answer.