问题
根据定积分的基本性质，$\textcolor{Orange}{\int_{a}^{b}}$ $\textcolor{Orange}{[}$ $\textcolor{Orange}{f(x)}$ $\textcolor{White}{+}$ $\textcolor{Orange}{g(x)}$ $\textcolor{Orange}{]}$ $\textcolor{Orange}{\mathrm{d} x}$ $=$ $?$选项
[A]. $\int_{a}^{b}$ $[$ $f(x)$ $+$ $g(x)$ $]$ $\mathrm{d} x$ $=$ $\int_{a}^{b}$ $f(x)$ $\mathrm{d} x$ $\times$ $\int_{a}^{b}$ $g(x)$ $\mathrm{d} x$[B]. $\int_{a}^{b}$ $[$ $f(x)$ $+$ $g(x)$ $]$ $\mathrm{d} x$ $=$ $\int_{a}^{b}$ $f(x)$ $\mathrm{d} x$ $-$ $\int_{a}^{b}$ $g(x)$ $\mathrm{d} x$
[C]. $\int_{a}^{b}$ $[$ $f(x)$ $+$ $g(x)$ $]$ $\mathrm{d} x$ $=$ $\int_{a}^{b}$ $f(x)$ $\mathrm{d} x$ $+$ $\int_{a}^{b}$ $g(x)$ $\mathrm{d} x$
[D]. $\int_{a}^{b}$ $[$ $f(x)$ $+$ $g(x)$ $]$ $\mathrm{d} x$ $=$ $\int_{b}^{a}$ $f(x)$ $\mathrm{d} x$ $+$ $\int_{b}^{a}$ $g(x)$ $\mathrm{d} x$
$$\int_{\textcolor{Green}{a}}^{\textcolor{Green}{b}} [\textcolor{Orange}{f(x)} \textcolor{Red}{+} \textcolor{Orange}{g(x)}] \mathrm{d} x =$$ $$\int_{\textcolor{Green}{a}}^{\textcolor{Green}{b}} \textcolor{Orange}{f(x)} \mathrm{d} x \textcolor{Red}{+} \int_{\textcolor{Green}{a}}^{\textcolor{Green}{b}} \textcolor{Orange}{g(x)} \mathrm{d} x.$$