sum of integrals over patial intervals != integral over whole interval

*To*: mathgroup at smc.vnet.net*Subject*: [mg71719] sum of integrals over patial intervals != integral over whole interval*From*: Peter Pein <petsie at dordos.net>*Date*: Mon, 27 Nov 2006 04:04:49 -0500 (EST)

Dear group, I wanted Mathematica to show, that for f[x_]:=Log[Sin[x]^2]Tan[x], Integrate[f[x],{x,0,Pi}]==0, because f[x]+f[Pi-x]==0. Mathematica says Integrate[f[x],{x,0,Pi}] does not converge, but Integrate[f[x],{x,0,Pi/2}] and Integrate[f[x],{x,Pi/2,Pi}] evaluate to -Pi^2/12 resp. P^2/12 and the sum is zero. The more general integral Integrate[f[x],{x,0,z},Assumptions->Pi/2<z<=Pi] evaluates explicitly (?). What did I do wrong? http://people.freenet.de/Peter_Berlin/Mathe/komisch.nb TIA, Peter