问题
已知，有向曲线弧 $L$ 可分成两段光滑的有向曲线弧 $L_{1}$ 和 $L_{2}$, 则 $\int_{L}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $?$选项
[A]. $\int_{L}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\int_{\frac{1}{L_{1}}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $+$ $\int_{\frac{1}{L_{2}}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$[B]. $\int_{L}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\int_{L + L_{1}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $+$ $\int_{L + L_{2}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$
[C]. $\int_{L}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\int_{L_{1}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $-$ $\int_{L_{2}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$
[D]. $\int_{L}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\int_{L_{1}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $+$ $\int_{L_{2}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$
$\int_{L}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\int_{L_{1}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $+$ $\int_{L_{2}}$ $\boldsymbol{F}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$