问题
已知 $\alpha$ 和 $\beta$ 为常数，则，根据第一类曲线积分中常数的运算性质，以下选项中正确的是哪个？选项
[A]. $\int_{L}$ $\big[$ $\alpha$ $f(x, y)$ $\pm$ $\beta$ $g(x, y)$ $\big]$ $\mathrm{d} s$ $=$ $\frac{1}{\alpha}$ $\int_{L}$ $f(x, y)$ $\mathrm{d} s$ $\pm$ $\frac{1}{\beta}$ $\int_{L}$ $g(x, y)$ $\mathrm{d} s$[B]. $\int_{L}$ $\big[$ $\alpha$ $f(x, y)$ $\pm$ $\beta$ $g(x, y)$ $\big]$ $\mathrm{d} s$ $=$ $\alpha$ $\int_{L}$ $f(x, y)$ $\mathrm{d} s$ $\times$ $\beta$ $\int_{L}$ $g(x, y)$ $\mathrm{d} s$
[C]. $\int_{L}$ $\big[$ $\alpha$ $f(x, y)$ $\pm$ $\beta$ $g(x, y)$ $\big]$ $\mathrm{d} s$ $=$ $\alpha$ $\int_{L}$ $f(x, y)$ $\mathrm{d} s$ $\mp$ $\beta$ $\int_{L}$ $g(x, y)$ $\mathrm{d} s$
$\int_{L}$ $\big[$ $\alpha$ $f(x, y)$ $\pm$ $\beta$ $g(x, y)$ $\big]$ $\mathrm{d} s$ $=$ $\alpha$ $\int_{L}$ $f(x, y)$ $\mathrm{d} s$ $\pm$ $\beta$ $\int_{L}$ $g(x, y)$ $\mathrm{d} s$~$\int_{L}$ $\big[$ $\alpha$ $f(x, y)$ $\pm$ $\beta$ $g(x, y)$ $\big]$ $\mathrm{d} s$ $=$ $\alpha$ $\int_{L}$ $f(x, y)$ $\mathrm{d} s$ $\pm$ $\beta$ $\int_{L}$ $g(x, y)$ $\mathrm{d} s$