In the meantime, for those too enthralled to wait, let me guess at the main results: ......

You realised that the electric field $\displaystyle \vec{E}$ was conservative (by checking whether $\displaystyle \nabla \times \vec{E} = 0$) and therefore:

1. Could be expressed in the form $\displaystyle \vec{E} = \nabla V$, and

2. Is independent of the path between the two points.

Then you got $\displaystyle V = 2x^3y + y^2$ and hence found that $\displaystyle

V_{(x, y)} - V_{(0, 0)} = \int_{(0, 0)}^{(x, y)} E \cdot dl = 2x^3 y + y^2$.

The details

*will* be of interest to others.