问题
若函数 $\textcolor{Orange}{F(x)}$ 和 $\textcolor{Orange}{M(x)}$ 在区间 $[a, b]$ 上具有连续的导函数 $\textcolor{Orange}{F ^{\prime}(x)}$ 和 $\textcolor{Orange}{M ^{\prime}(x)}$, 则以下关于定积分 $\textcolor{Orange}{\int_{a}^{b}}$ $\textcolor{Orange}{F(x)}$ $\textcolor{Orange}{M ^{\prime}(x)}$ $\textcolor{Orange}{\mathrm{d} x}$ 的结论中，正确的是哪个？选项
[A]. $\int_{a}^{b}$ $F(x)$ $M ^{\prime}(x)$ $\mathrm{d} x$ $=$ $F ^{\prime}(x)$ $M ^{\prime}(x)$ $|_{a}^{b}$ $-$ $\int_{a}^{b}$ $F ^{\prime}(x)$ $M(x)$ $\mathrm{d} x$[B]. $\int_{a}^{b}$ $F(x)$ $M ^{\prime}(x)$ $\mathrm{d} x$ $=$ $F(x)$ $M(x)$ $|_{a}^{b}$ $-$ $\int_{a}^{b}$ $F(x)$ $M ^{\prime}(x)$ $\mathrm{d} x$
[C]. $\int_{a}^{b}$ $F(x)$ $M ^{\prime}(x)$ $\mathrm{d} x$ $=$ $F(x)$ $M(x)$ $|_{a}^{b}$ $-$ $\int_{a}^{b}$ $F ^{\prime}(x)$ $M(x)$ $\mathrm{d} x$
[D]. $\int_{a}^{b}$ $F(x)$ $M ^{\prime}(x)$ $\mathrm{d} x$ $=$ $F(x)$ $M(x)$ $|_{a}^{b}$ $+$ $\int_{a}^{b}$ $F ^{\prime}(x)$ $M(x)$ $\mathrm{d} x$
$$\int_{\textcolor{Orange}{a}}^{\textcolor{Orange}{b}} \Bigg[ \textcolor{Red}{F}(x) \textcolor{Green}{\cdot} \textcolor{Red}{M} ^{\textcolor{Yellow}{\prime}}(x) \Bigg] \mathrm{d} x =$$ $$\Bigg[ \textcolor{Red}{F}(x) \textcolor{Green}{\cdot} \textcolor{Red}{M}(x) \Bigg] \Bigg|_{\textcolor{Orange}{a}}^{\textcolor{Orange}{b}}$$ $$\textcolor{Green}{-}$$ $$\int_{\textcolor{Orange}{a}}^{\textcolor{Orange}{b}} \Bigg[ \textcolor{Red}{F} ^{\textcolor{Yellow}{\prime}}(x) \textcolor{Green}{\cdot} \textcolor{Red}{M}(x) \Bigg] \mathrm{d} x.$$