Evaluate the following:$\int\limits_ {\Large\frac{-\pi}{4}}^{\Large\frac{\pi}{4}} \log(\sin x+\cos x)dx$

Question

$\begin{array}{1 1} (A) \large\frac{\pi}{2}\log\large\frac{1}{2} \\ (B) \large\frac{\pi}{4}\log\large\frac{1}{2} \\(C) \large\frac{\pi}{2}\log 2 \\ (D) \large\frac{\pi}{4}\log 2 \end{array} $