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Defining symmetric functions

If you ask for
Sin[x] + Sin[-x]
Mathematica correctly says 0. Now I would like to let mathematica
simplify an integral involving some unknown symmetric functions.
So mathematica should be able to set
Integral[symm[x], {x,-1,1}] to be equal zero, without knowing how
symm[x] looks exactly.
How should I do this? w[x_] := w[-x] gives me too many recursions and
using restrictions on patterns like /; x>0 doesn't help also.

Thanks in advance,
Axel Thimm   thimm at thimm at

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