Van't hoff equation integration

hey guys i understand this question but all I really want to know is why when integrating the van't hoff equation, why are the the equilibrium constant values (K) the 2 numbers on the left hand side of the integral and why are the 2 temperatures on the right hand side on the equation. How do you exactly know which numebers go where?

https://imgur.com/a/bDCtPlK - hopefully u guys can see this imgur link

You're integrating with respect to temperature in the right and with respect to ln(Kp) on the left. The limits are the values of those variables.

The top number of the intergral is b and the bottom is a when you sub back in after the intergration you do b minus a, on the left hand side you use log laws that's why it's divide

How do you know exactly you're integrating wrt to ln(Kp) on the left and integrating wrt to temp on the right? It doesn't specifically say

Sorry the way i worded the question was poor

How do you know exactly you're integrating wrt to ln(Kp) on the left and integrating wrt to temp on the right? It doesn't specifically say