Umberto Zannier, of the Scuola Normale Superiore, surveys a question George Polya posed around 1921 about the algebraicity of the indefinite integral of an algebraic function, framed in terms of the integrality of coefficients in its power-series expansion. Zannier traces Polya's own solution for rational functions, built on Fermat's congruence, through to the much later resolution of the general case by transcendence techniques. He connects the problem to Grothendieck's local-global conjecture on linear differential equations over polynomial rings and to related number-theoretic questions, then introduces a newer question arising from an alternative approach to Polya's original issue, along with answers supplied more recently by Nicholas Katz. Time permitting, he sketches a recent argument strengthening the main results. Delivered as part of the Institute for Advanced Study's Special Year Learning Seminar, the talk is aimed at an audience already fluent in algebraic and transcendental number theory.