问题
若 $x$ $\in$ $[a, b]$, 且 $\textcolor{Red}{f(x)}$ $\textcolor{Red}{\geqslant}$ $\textcolor{Red}{0}$, 则以下关于定积分 $\textcolor{Orange}{\int_{a}^{b}}$ $\textcolor{Orange}{f(x)}$ $\textcolor{Orange}{\mathrm{d} x}$ 的结论，正确的是哪个？选项
[A]. $\int_{a}^{b}$ $f(x)$ $\mathrm{d} x$ $\geqslant$ $0$[B]. $\int_{a}^{b}$ $f(x)$ $\mathrm{d} x$ $\neq$ $0$
[C]. $\int_{a}^{b}$ $f(x)$ $\mathrm{d} x$ $=$ $0$
[D]. $\int_{a}^{b}$ $f(x)$ $\mathrm{d} x$ $\leqslant$ $0$
$$\textcolor{Orange}{f(x)} \textcolor{Red}{\geqslant} \textcolor{Orange}{0} \textcolor{Green}{\Rightarrow}$$ $$\int_{a}^{b} \textcolor{Orange}{f(x)} \mathrm{d} x \textcolor{Red}{\geqslant} \int_{a}^{b} \textcolor{Orange}{0} \mathrm{d} x \textcolor{Green}{\Rightarrow}$$ $$\int_{a}^{b} \textcolor{Orange}{f(x)} \mathrm{d} x \textcolor{Red}{\geqslant} \textcolor{Orange}{0}.$$
同理可知：
若 $\textcolor{Orange}{f(x)}$ $\textcolor{Red}{\leqslant}$ $\textcolor{Orange}{0}$, 则：$$\int_{a}^{b} \textcolor{Orange}{f(x)} \mathrm{d} x \textcolor{Red}{\leqslant} \textcolor{Orange}{0}.$$