6. Given the function $f(x)=2 \sin x-\sin 2 x+\sqrt{3}$, which of the following statements is incorrect?
A. $f(x)$ has two zeros in $[-\pi, \pi]$
C. The minimum value of $f(x)$ is $-\sqrt{3}$
B. The graph of $f(x)$ is symmetric about the point $(\pi, \sqrt{3})$
D. The maximum value of $f(x)$ is $\frac{5 \sqrt{3}}{2}$
$$
f^{\prime}(x)=2 \cos x-2 \cos 2 x=-2\left(2 \cos ^{2} x-\cos x-1\right)=-2(2 \cos x+1)(\cos x-1) \text {, }
$$

Then $f(x)$ is monotonically increasing on $\left[2 k \pi-\frac{2 \pi}{3}, 2 k \pi+\frac{2 \pi}{3}\right]$, and monotonically decreasing on $\left[2 k \pi+\frac{2 \pi}{3}, 2 k \pi+\frac{4 \pi}{3}\right]$, i.e., $f(x)_{\min }=f\left(-\frac{2 \pi}{3}\right)=-\frac{\sqrt{3}}{2}, f(x)_{\max }=f\left(\frac{2 \pi}{3}\right)=\frac{5 \sqrt{3}}{2}$. Therefore, the answer is $C$.