My textbook has the following question

What is the potential difference between two points that are 50cm and 80cm respectively from a point charge of 2uC?

Unfortunately, the textbook has not taught me how to actually do this sort of question, as I only know that $V = ΔU/q$ which is about energy not distance. Using my own inference, I took the potential difference to be the area under the field-distance graph between the two points as this would essentially be equal to the work done on a charge when it is moved between the two points.

By integrating $E = kQ/r^2$ I came to the equation $V = kQ(1/a - 1/b)$ where a and b are two distances. This gives an answer of 13500V.

However, the textbook answer is 44 000V, which is obtained by directly subtracting the value of E at 80cm from the value of E at 50cm ($V = kQ/0.5^2 - kQ/0.8^2)$. I fail to see how the textbook answer is correct - for example, you do not calculate the amount of work done between two points simply by subtracting the force at the points? Isn't this a similar problem?

Am I correct or is my textbook correct, and why?