What are the rules for evaluating an indefinite integral by by expanding the integrand in power series and integrating the power series term by term.

Question

I was browsing through Carr's Synopsis, the book made famous by Srinivasa Ramanujan (available in archive.org), in page 319 . I found this:

We usually integrate only definite integrals term by term, subject to some conditions. Are there conditions for indefinite integrals also? This is a problem in differential algebras, not calculus, I suppose.