Considering the following scenario:
When calculating the electric field on the axis of a ring charge, you end up with:
And following the integration:
I am trying to understand the idea of $\int dq$ and how it evaluates to $Q$. I understand that integrating an infinitesimal like how $\int dx = x + C$ works, but I don't quite understand the idea of integration of these $dq$ terms with the ring being of finite $2(\pi)(a)$ in circumference. Why are we able to do this integral and know that it's integrating exactly once around the ring (summing an infinite amount of infinitesimal charges on each point of the circumference), not an infinite amount of times around the ring, as it doesn't have limits?