Cho tích phân

Câu hỏi: Cho tích phân $I={\int }_0^{\frac{\mathrm{\pi }}{4}}\left(x-1\right)\sin 2xdx$. Tìm đẳng thức đúng

A. $I=-\left(x-1\right){\overline{)\cos 2x}}_0^{\frac{\mathrm{\pi }}{4}}+{\int }_0^{\frac{\mathrm{\pi }}{4}}\cos 2xdx$

B. $I=-\left(x-1\right)cos2x-{\int }_0^{\frac{\mathrm{\pi }}{4}}\cos 2xdx$

C. $I=-\frac{1}{2}\left(x-1\right){\overline{)\cos 2x}}_0^{\frac{\mathrm{\pi }}{4}}+\frac{1}{2}{\int }_0^{\frac{\mathrm{\pi }}{4}}\cos 2xdx$

D. $I=-\frac{1}{2}\left(x-1\right){\overline{)\cos 2x}}_0^{\frac{\mathrm{\pi }}{4}}-{\int }_0^{\frac{\mathrm{\pi }}{4}}\cos 2xdx$