If you change your variable what do you need to do to the limits ?

If you change the variable you need to change the limits, thinking about it like this. If you are initially integrating x^2 from 3 to 6, and you substitute u=x^2 (you shouldn’t do this for this integral but it’s just for use as an example), then it’s better to think about the initial integral as integrating x^2 from x=3 to x=6; so when you calculate the integral in terms of u, it needs to be with limits u= something and u= something, in this case your limits would become u = 3^2 = 9 to u = 6^2 = 36.