# Is this a contour integral question?

I had this in my previous cats that I'm not sure whether it's really a complex analysis question, looks like a differential question with line integrals a bit

$$\int_{(1,3)}^{(4,5)} (2y+x^2)\,dx + (3x-y)\,dy$$

I was thinking the closest concept would be contour integration axis-wise i.e horizontally then vertically, such that the gradient of the line is $y=(7+2x)/3$ which when you replace in the expressions you would get something like:

$$\int_{(1,3)}^{(4,5)} (7/3+2/3x)+x^2)\,dx + \int_{(1,3)}^{(4,5)} (9/2y-21/2-y) \, dy$$

Is this the right way?

\begin{align} \color{#f00}{2} & = \partiald{\pars{2y + x^{2}}}{y} \color{#f00}{\not=} \partiald{\pars{3x - y}}{x} = \color{#f00}{3} \end{align} So, your result will be $\color{#f00}{path\ dependent}$.