I will review integration with respect to Euler characteristic in the constructible category (a simple combinatorial integration theory). Then, I will present an extension to the class of real-valued integrands, definable with respect to an o-minimal structure. This extension, though ostensibly more analytic, has a deeper connection to Morse theory. No previous exposure to o-minimal topology/geometry or Euler integration assumed. The talk will end with some conjectural thoughts about Morse theory for distributions.