Finding Potential Function
As a resource, refer to the German wikipedia page at https://de.wikipedia.org/wiki/Elektrische_Spannung which I find a bit more illuminating than the English one at https://en.wikipedia.org/wiki/Voltage
Your top formula is for potential. In the form of a definite integral, it would be as follows:

(We are concerned with the conservative field, so omit the EMF portion with dA/dt)
Voltage is defined based on work required by an electron in an electrical field to move from A to B

which lines up with your bottom formula.
Putting the two together,