${\int }_{-2}^2 \left|\right[\mathrm{x}\left]\right|\mathrm{dx}$ is equal to

Solution:

$\begin{array}{l}{\int }_{-2}^2 \left|\right[\mathrm{x}\left]\right|\mathrm{dx}\\ ={\int }_{-2}^{-1} \left|\right[\mathrm{x}\left]\right|\mathrm{dx}+{\int }_{-1}^0 \left|\right[\mathrm{x}\left]\right|\mathrm{dx}+{\int }_0^1 \left|\right[\mathrm{x}\left]\right|\mathrm{dx}+{\int }_1^2 \left|\right[\mathrm{x}\left]\right|\mathrm{dx}\\ ={\int }_{-2}^{-1} 2\mathrm{dx}+{\int }_{-1}^0 1\mathrm{dx}+{\int }_0^1 0\mathrm{dx}+{\int }_1^2 1\mathrm{dx}\\ =2[\mathrm{x}{]}_{-2}^{-1}+[\mathrm{x}{]}_{-1}^0+0+[\mathrm{x}{]}_1^2\\ =2(-1+2)+(0+1)+(2-1)\\ =2+1+1=4\end{array}$