I will discuss a result of Arias-Abad and Schaetz, originally due to Gugenheim, in which they construct an A_{\infty}-algebra generalization of the standard De Rham theorem. In particular, they promote the standard integration map going from the De Rham complex on a smooth manifold to the differential graded algebra of singular cochains on the manifold, which induces an isomorphism in cohomology, to an A_{\infty}-quasi-isomorphism between these DGAs. This map is constructed by combining two pieces of machinery: the iterated integral, originally due to Chen, and the so-called Igusa map. This talk will discuss both of these constructions, and will conclude by combining them to arrive at the A_{\infty} De Rham theorem.