JEE Math Practice Question

Let $$f:R \to R$$ be a function defined by : $$f(x) = \left\{ {\begin{matrix} {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2} \\ {{x^2} + 2x - 6} & ; & {2 5} \\ \end{matrix} } \right.$$ 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 $$I = \int\limits_{ - 2}^2 {f(x)\,dx} $$. Then the ordered pair (m, I) is equal to :

1. A.$$\left( {3,\,{{27} \over 4}} \right)$$
2. B.$$\left( {3,\,{{23} \over 4}} \right)$$
3. C.$$\left( {4,\,{{27} \over 4}} \right)$$
4. D.$$\left( {4,\,{{23} \over 4}} \right)$$