Let a and b be real constants such that the function f defined by \(f(x)= \rm \left\{ \begin{matrix} \rm x^2+3x+a, & \rm x\le1 \\\ \rm bx+2, & \rm x>1\end{matrix}\right.\) be differentiable on R., then the value of \( \int_{-2}^2f(x)d x\) is
1
\(\frac{15}{6}\)
2
\(\frac{19}{6}\)
3
21
4
17