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 \(4I-1\).