[Physics] If electric field is conservative then line integral along closed path is zero, then why is potential not zero

Question

Here in the first image it is said $\displaystyle \int_a ^b E\cdot \mathrm dl\,$ is $0 $:

Here in the second image it looks like $\displaystyle \int_a ^b E\cdot \mathrm dl\,$ is not $0$:

If field is conservative which it is here, then closed line integral is 0 which is the case in the first image, but the potential is also a line integral so why is it not 0

Please help me understand this!

Answer 1

The integral around any closed path is zero. But $\vec{a}$ and $\vec{b}$ are not the same point: the path is not closed, so the integral does not have to be zero.