The integral $\Large \int \limits_{\normalsize 0}^{\normalsize \pi} $$ \sqrt{1 + 4 \sin^2\large\frac{x}{2} \normalsize- \normalsize 4 \normalsize\sin \large\frac{x}{2}}$$\;dx$

Question

$\begin{array}{1 1} (A) \;\pi -4 \\ (B) \;\frac{2\pi}{3}-4-4\sqrt3 \\ (C) \;4\sqrt 3 - 4 \\ (D) \;4\sqrt 3 - 4-\large\frac{\pi}{3} \end{array} $