Cho tích phân \(I = \int\limits_0^{\frac{\pi }{4}} {\left( {x - 1} \right)\sin 2xdx.} \) Tìm đẳng thức đúng?

A. \(I =  - \left( {x - 1} \right)cos2x - \int\limits_0^{\frac{\pi }{4}} {cos2xdx.} \)

B. \(I =  - \frac{1}{2}\left( {x - 1} \right)cos2x\left| \begin{array}{l}
^{\frac{\pi }{4}}\\
_0
\end{array} \right. - \int\limits_0^{\frac{\pi }{4}} {cos2xdx.} \)

C. \(I =  - \frac{1}{2}\left( {x - 1} \right)cos2x\left| \begin{array}{l}
^{\frac{\pi }{4}}\\
_0
\end{array} \right. + \frac{1}{2}\int\limits_0^{\frac{\pi }{4}} {cos2xdx.} \)

D. \(I =  - \left( {x - 1} \right)cos2x\left| \begin{array}{l}
^{\frac{\pi }{4}}\\
_0
\end{array} \right. + \int\limits_0^{\frac{\pi }{4}} {cos2xdx.} \)