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 $$4I-1$$.