Let a and b be real constants such that the function f defined by f(x)= {x^2+3 x+a, x ≤ 1; b x+2, x>1} be differentiable on R. Then, the value of…

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