Constructible functions and motivic integration I. We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative framework, in which we develop a relative version of motivic integration. To cite this article: R. Cluckers, F. Loeser, C. R. Acad. Sci. Paris, Set. I 339 (2004). (C) 2004 Academie des sciences. Publie par Elsevier SAS. Tous droits reserves.