polar coordinates-changing bounds of integration

When I change the integral to polar form, how do i adjust the bounds of integration? Do i have to look at the graph of the new function and determine r and theta from that? or is there a formula to do so? i mean i how to change x and y into rcostheta and rsintheta. but the bounds of integration for theta always involve pi, which i can't get from just some number.

i don't have a specific example, but say the bounds of integration for theta were -3 to 3. is there a formulaic way of figuring out the new bounds, or would i need to look at the graph of the function to determine that?

and when changing the bounds for r, same question basically. is it just using x=rcostheta, etc. or is it using the graph to see where r goes?

thanks for any help