$\text{ If }\mathrm{I}={\int }_{-20\mathrm{\pi }}^{20\mathrm{\pi }} |\sin \mathrm{x}|[\sin \mathrm{x}]\mathrm{dx}\text{ (where [.] }$ denotes the greatest integer function), then the value of I is___ 

$$\begin{gathered} \mathrm{I}={\int }_{-20\mathrm{\pi }}^{20\mathrm{\pi }} |\sin \mathrm{x}|[\sin \mathrm{x}]\mathrm{dx} \\ ={\int }_{-20\mathrm{\pi }}^0 |\sin \mathrm{x}|[\sin \mathrm{x}]\mathrm{dx}+{\int }_0^{20\mathrm{\pi }} |\sin \mathrm{x}|[\sin \mathrm{x}]\mathrm{dx} \\ =-{\int }_{20\mathrm{\pi }}^0 |\sin \mathrm{x}|[-\sin \mathrm{x}]\mathrm{dx}+{\int }_0^{20\mathrm{\pi }} |\sin \mathrm{x}|[\sin \mathrm{x}]\mathrm{dx} \\ ={\int }_0^{20\mathrm{\pi }} |\sin \mathrm{x}|\left(\right[\sin \mathrm{x}]+[-\sin \mathrm{x}\left]\right)\mathrm{dx} \\ =20{\int }_0^{\mathrm{\pi }} |\sin \mathrm{x}|\left(\right(-1\left)\right)\mathrm{dx} \\ =-20{\int }_0^{\mathrm{\pi }} |\sin \mathrm{x}|\mathrm{dx} \\ =-20{\int }_0^{\mathrm{\pi }} \sin \mathrm{xdx} \\ =-40{\int }_0^{\frac{\mathrm{\pi }}{2}} \sin \mathrm{xdx} \\ =-40 \end{gathered}$$