Integrate : $\int \large\frac{\sin x}{\sin (x-\alpha)}$$dx$

Question

$$\begin {array} {1 1} (a)\;x \cos \alpha + \sin \alpha \log | \sin (x - \alpha)| +c \\ (b)\;x \cos \alpha + \sin \alpha +c \\ (c)\;x \sin \alpha + \sin \alpha \log | \sin (x - \alpha)| +c\\ (d)\;None \end {array}$$