Looking for a good problem book for PROOF-BASED integration

[mathboy]

Looking for a good book for PROOF-BASED integration

Just to be clear, I'm not looking for a book that helps you to exercise calculating integrals, but more like problems that involve doing proofs involving integrals. Theoretical and abstract integration problems like the ones in this thread:

https://www.physicsforums.com/showthread.php?t=36033

Any good recommendation for these types of integration problems?

 

[rudinreader]

Integration is usually around chapter 6. If you suddenly got the interest in a deeper understanding of the integral the bad news is that it is difficult for most people to skip the first 75% of undergraduate analysis to get to the good part.
But the good news is that if you have a good motivation for studying analysis, the chances are better that you can get through the book (to chapter 6) more quickly. You should at least spend a month on it (and that would be a minimum in the case you are very good at it!).

As for a book, Baby Rudin is the one I read, so that is the one I recommend.

 

[rohanprabhu]

I use 'Integral Calculus' by P. Shanti Narayan. It has lots of exercises with each exercise succeeded by Illustrated examples and proof of the identities used in subsequent exercise.

 

[zhentil]

Riemann integration is fairly trivial once you build the machinery. The only interesting questions (in chapter 6 of rudin, at least) are just frustrating since they're much easier with the Lebesgue integral.