Definite Integration

Let \(a\) and \(b\) be real constants such that the function \(f\) defined by $$f(x)=\left\{\begin{array}{ll}x^2+3 x+a & , x \leq 1 \\ b x+2 & , x>1\end{array}\right.$$ be differentiable on \(\mathbb{R}\). Then, the value of \(\int_\limits{-2}^2 f(x) d x\) equals