Let $F:R\to R$ be a thrice differentiable function. Suppose that $F\left(1\right)=0, F\left(3\right)=-4$ and $F^{\prime }\left(x\right)<0$ for all $x\in \left(\frac{1}{2}, 3\right).$ Let $f\left(x\right)=xF\left(x\right)$ for all $x\in R$. If $\underset{1}{\overset{3}{\int }}{x}^2{F}^{\prime }\left(x\right)dx=-12$ and $\underset{1}{\overset{3}{\int }}{x}^3 F^{\prime \prime }\left(x\right)dx=40,$ then the correct expression(s) is(are)