An architectural feature for a new gallery is designed with a side profile following the curve $y=\frac{3}{2}{x}^3$. To calculate the volume of concrete required, an engineer first determines the total cross-sectional area between the curve and the $x$-axis for two distinct sections:

Section A is bounded by the curve, the $x$-axis, and the vertical lines $x=-3$ and $x=-1$.

Section B is bounded by the curve, the $x$-axis, and the vertical lines $x=2$ and $x=4$.