The function $f: \mathbb{R} \rightarrow \mathbb{R}$ is defined as
$$f(x) = \begin{cases} 2\sin x, & \text{if } \sin x \geq 0 \\ 0, & \text{if } \sin x < 0 \end{cases}$$
Accordingly, which of the following is the image of the open interval $(-\pi, \pi)$ under $f$?
A) $[-2,2]$\\
B) $(-1,2)$\\
C) $[0,1]$\\
D) $(0,2)$\\
E) $[0,2]$