Chọn B
\(y'=m^{2} +2m+1-\left(m^{2} -m+1\right)\sin x. \)
Hàm số đồng biến trên \(\left(0;2\pi \right) \Leftrightarrow y'\ge 0,\forall x\in \left(0;2\pi \right). \)
\(\Leftrightarrow m^{2} +2m+1-\left(m^{2} -m+1\right)\sin x\ge 0\forall x\in \left(0;2\pi \right) \)
\(\Leftrightarrow \sin x\le \frac{m^{2} +2m+1}{m^{2} -m+1} \forall x\in \left(0;2\pi \right) \)
\(\Leftrightarrow 1\le \frac{m^{2} +2m+1}{m^{2} -m+1} \Leftrightarrow m^{2} -m+1\le m^{2} +2m+1\Leftrightarrow m\ge 0. \)