$\int \limits_0^{\pi/2} \large\frac{200 \sin x+100 \cos x}{\sin x+\cos x}$$dx$ is equal to :

Question

$$\begin {array} {1 1} (a)\;50 \pi & \quad (b)\;25 \pi \\ (c)\;75 \pi & \quad (d)\;150 \pi \end {array}$$