Let \( f(x)=2+|x|-|x-1|+|x+1|,\, x\in \mathbb{R} \).
Consider
\((S1):\;\displaystyle f'\!\left(-\frac{3}{2}\right)+f'\!\left(-\frac{1}{2}\right)+f'\!\left(\frac{1}{2}\right)+f'\!\left(\frac{3}{2}\right)=2\)
\((S2):\; \displaystyle\int\limits_{-2}^{2} f(x)\,dx = 12\)
Then,
