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May 2, 2013 at 1:00 comment added D M Great! Numerical experiments suggest that for $g(x)=1/(1+x^2)$, the integral tends to a nonzero constant, so the limit is optimal. Thanks very much.
May 2, 2013 at 0:54 vote accept D M
May 1, 2013 at 16:33 history edited ioannis.parissis CC BY-SA 3.0
The argument was changed completely to a simpler (and more efficient one) so I erased my original answer.
Apr 30, 2013 at 20:49 history edited ioannis.parissis CC BY-SA 3.0
added 73 characters in body
Apr 30, 2013 at 20:41 history answered ioannis.parissis CC BY-SA 3.0