this is a pretty basic problem, but how do you compute an integral over a vector $\vec{r}=\left({x,y}\right)$? Using this as an example:$$\int_{\vec{r_1}}^{\vec{r_2}}(x,xy^2)\cdot d\vec{r}$$ I‘m aware that $$\int_{\vec{r_1}}^{\vec{r_2}}(x,xy^2)\cdot d\vec{r}=\left(\int_{\vec{r_1}}^\vec{r_2}x\cdot d\vec{r},\int_{\vec{r_1}}^\vec{r_2}xy^2\cdot d\vec{r}\right),$$ but I don’t know how to continue and how to integrate over $\vec{r}$, since there‘s two variables involved I can integrate over.
Thank you!