If \[\int_{{}}^{{}}{(\cos x-\sin x)\ dx=\sqrt{2}\sin (x+\alpha )+c}\], then \[\alpha =\]

If \[\int_{{}}^{{}}{(\cos x-\sin x)\ dx=\sqrt{2}\sin (x+\alpha )+c}\],

1.	If \[\int_{{}}^{{}}{(\cos x-\sin x)\ dx=\sqrt{2}\sin (x+\alpha )+c}\], then \[\alpha =\]
A.	\[\frac{\pi }{3}\]
B.	\[-\frac{\pi }{3}\]
C.	\[\frac{\pi }{4}\]
D.	\[-\frac{\pi }{4}\]
Answer» D. \[-\frac{\pi }{4}\]