In a more complicated expression I would like Mathematica to simplify
Integrate[f[x - Floor[x]], {x, 0, 1}]
to
Integrate[f[x], {x, 0,1 }]
Simplify[…] doesn’t seem to do it. Ideas? Thanks.
Use correct assumptions, probably before calling Integrate:
Simplify[f[x - Floor[x]], 0 <= x <= 1]
(* f[x - Floor[x]] *)
… but:
Simplify[f[x - Floor[x]], 0 <= x < 1]
(* f[x] *)
You can also try Assumptions option in Integrate itself.