Unexpected condition on convergence of integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg67293] Unexpected condition on convergence of integral*From*: Andrew Moylan <andrew.moylan at anu.edu.au>*Date*: Fri, 16 Jun 2006 00:27:17 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Integrate[1 / (1 + (x - y)^2), {y, -Infinity, Infinity}] yields If[Im[x] != 0, Pi, ...], but (I think) this integral should converge to Pi unconditionally (try it for some real values of x). Using the option "Assumptions -> Im[x] == 0" in Integrate[] further yields the following warning: "Integral of [bla] does not converge on {-Infinity, Infinity}". Can anyone shed some light on why Integrate can't determine that this integral converges for all x?