\[\int_{{}}^{{}}{\sqrt{1+\sin x}\ dx=}\] [MP PET 1995]

• A. \[\frac{1}{2}\left( \sin \frac{x}{2}+\cos \frac{x}{2} \right)+c\]
• B. \[\frac{1}{2}\left( \sin \frac{x}{2}-\cos \frac{x}{2} \right)+c\]
• C. \[2\sqrt{1+\sin x}+c\]
• D. \[-2\sqrt{1-\sin x}+c\]