Feynman integrals and motives

In Deligne et al. 1999, Tome I, p. 413, P. Deligne writes "The technique of Feynman graphs allows one to write down an asymptotic series for the function integral of a conformal field theory in a neighborhood of a free quantum field theory". This is beyond the power of the author of the proposal to explain  those lines in details, but  it makes clear that Feynman integrals, that is integrals formed with a specific rule out of specific graphs called Feynman graphs, may be of interest from a purely mathematical viewpoint.