1.
Let aa and bb be real constants such that the function ff defined by
f(x)={x2+3x+a,x1bx+2,x>1f(x)=\begin{cases}x^2+3x+a, & x\le 1\\ bx+2, & x>1\end{cases}
is differentiable on R\mathbb{R}. Then the value of 02f(x)dx\displaystyle\int_0^2 f(x)\,dx equals