Let $\mathrm{a}$ and $\mathrm{b}$ be real constants such that the function $f$ defined by $f\left(x\right)=\left\{\begin{array}{cc}{x}^2+3x+a,& x\le 1\\ bx+2,& x>1\end{array}\right.$ be differentiable on $R$. Then, the value of ${\int }_{-2}^{2}f\left(x\right)dx$ equals