If the area enclosed by $y=g\left(x\right),$ and the ordinates $x=-3,x=5$ and x-axis where g(x) is the inverse of $f\left(x\right)=x^3+3x+1$ is A, then [A] is_____ (where [.] denotes greatest integer function.)

Area bounded by the inverse functions with x-axis between the ordinates x = a and x = b is same as area bounded by the given function with y-axis between the ordinates y = a and y = b
$A=\underset{0}{\overset{1}{\int }}(5-(x^3+3x+1))dx+\underset{-1}{\overset{0}{\int }}((x^3+3x+1)+3)dx=\frac{9}{2}$