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