问题
以下关于无穷限的反常积分 $\textcolor{Orange}{\int_{- \infty}^{+\infty}}$ $\textcolor{Orange}{f(x)}$ $\textcolor{Orange}{\mathrm{d} x}$ 的结论中，正确的是哪个？选项
[A]. $\int_{- \infty}^{+\infty}$ $f(x)$ $\mathrm{d} x$ $=$ $\lim_{a \rightarrow + \infty}$ $\int_{a}^{c}$ $f(x)$ $\mathrm{d} x$ $+$ $\lim_{b \rightarrow – \infty}$ $\int_{c}^{b}$ $f(x)$ $\mathrm{d} x$[B]. $\int_{- \infty}^{+\infty}$ $f(x)$ $\mathrm{d} x$ $=$ $\lim_{a \rightarrow – \infty}$ $\int_{a}^{c}$ $f(x)$ $\mathrm{d} x$ $+$ $\lim_{b \rightarrow + \infty}$ $\int_{c}^{b}$ $f(x)$ $\mathrm{d} x$
[C]. $\int_{- \infty}^{+\infty}$ $f(x)$ $\mathrm{d} x$ $=$ $\lim_{a \rightarrow – \infty}$ $\int_{c}^{a}$ $f(x)$ $\mathrm{d} x$ $+$ $\lim_{b \rightarrow + \infty}$ $\int_{b}^{c}$ $f(x)$ $\mathrm{d} x$
[D]. $\int_{- \infty}^{+\infty}$ $f(x)$ $\mathrm{d} x$ $=$ $\lim_{a \rightarrow – \infty}$ $\int_{a}^{c}$ $f(x)$ $\mathrm{d} x$ $+$ $\lim_{b \rightarrow + \infty}$ $\int_{b}^{c}$ $f(x)$ $\mathrm{d} x$
$$\int_{\textcolor{Red}{- \infty}}^{\textcolor{Red}{+\infty}} f(x) \mathrm{d} x =$$
$$\int_{\textcolor{Red}{- \infty}}^{\textcolor{Yellow}{c}} f(x) \mathrm{d} x$$ $$\textcolor{Green}{+}$$ $$\int_{\textcolor{Yellow}{c}}^{\textcolor{Red}{+ \infty}} f(x) \mathrm{d} x =$$
$$\lim_{\textcolor{Yellow}{a} \textcolor{Green}{\rightarrow} \textcolor{Red}{- \infty}} \int_{\textcolor{Yellow}{a}}^{\textcolor{Yellow}{c}} f(x) \mathrm{d} x$$ $$\textcolor{Green}{+}$$ $$\lim_{\textcolor{Yellow}{b} \textcolor{Green}{\rightarrow} \textcolor{Red}{+ \infty}} \int_{\textcolor{Yellow}{c}}^{\textcolor{Yellow}{b}} f(x) \mathrm{d} x.$$