The value of $\int \limits_{\pi} ^{2 \pi} [ 2 \sin x]dx$ where [.] represents the greatest integer function , is

Question

$\begin{array}{1 1} \large\frac{-5 \pi}{3} \\ -\pi \\ \large\frac{5 \pi}{3} \\ -2 \pi \end{array} $