Integrate: $\int \limits_0^{2 \pi} \sqrt {1-\sin \large\frac{x}{2} } dx$

Question

\[\begin {array} {1 1} (a)\;8(\sqrt 2-1) \\ (b)\;4(\sqrt 2-1) \\ (c)\;2(\sqrt 2-1) \\ (d)\;None \end {array}\]