JEE Main 2022 — Definite Integration Question with Solution

Let $$f:R\to R$$ be a function defined by :

f(x) = \left\{ {\matrix{ {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2} \cr {{x^2} + 2x - 6} & ; & {2 < x < 3} \cr {[x - 3] + 9} & ; & {3 \le x \le 5} \cr {2x + 1} & ; & {x > 5} \cr } } \right.

where [t] is the greatest integer less than or equal to t. Let m be the number of points where f is not differentiable and $$I=\underset{-2}{\overset{2}{\int }}f(x)dx$$. Then the ordered pair (m, I) is equal to :