JEE-Advanced 2015 (6/40)

Calculus Level 4

Let $f:\mathbb{R} \to \mathbb{R}$ be a function defined by $f(x)=\begin{cases} \lfloor x \rfloor \ \ , \quad x \leq 2 \\ 0 \ \ , \quad x>2 \end{cases}$ If $I=\displaystyle \int_{-1}^2 \frac{xf(x^2)}{2+f(x+1)}\, dx$ , then find the value of $4I-1$ .