Let f: R → R be a function defined by: f(x)= {max_t ≤ x { t^3-3 t }; x ≤ 2; x^2+2 x-6; 2<x<3; [x-3]+9; 3 ≤ x ≤ 5; 2 x+1; x>5} where [ t ] is the…

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be a function defined by : $$f(x)=\left\{\begin{array}{cc} \max _{\mathbf{t} \leq x}\left\{\mathbf{t}^3-3 \mathbf{t}\right\} & ; x \leq 2 \\ x^2+2 x-6 & ; 2<x<3 \\ {[x-3]+9} & ; 3 \leq x \leq 5 \\ 2 x+1 & ; x>5 \end{array}\right. $$ where $\displaystyle [\mathrm{t}]$ is the greatest integer less than or equal to t . Let m be the number of points where $\displaystyle f$ is not differentiable and $\displaystyle \mathrm{I}=\int_{-2}^2 f(x) \mathrm{d} x$. Then the ordered pair ( $\displaystyle \mathrm{m}, \mathrm{I}$ ) is equal to :