Date: Jan 10, 2013 9:38 PM
Author: liquid.phynix@gmail.com
Subject: wrong result when computing a definite integral

hi group,

i run into this problem today when giving a bunch of easy integrals to mathematica.
here's a wolfram alpha link to the problem:
http://www.wolframalpha.com/input/?i=Integrate%5BExp%5BI+Sqrt%5B3%5Dy%5D%2C%7Bx%2C-2Pi%2C2Pi%7D%2C%7By%2C-Pi%2CPi%7D%5D#

the integrand does not depend on the 'x' variable, the inner integration should only result in a factor of 4Pi, and the correct result is a real number, yet the below integral gives a complex number which is far off from the correct value:
Integrate[Exp[I Sqrt[3] y], {x, -2 Pi, 2 Pi}, {y, -Pi, Pi}] -> -((4 I (-1 + E^(2 I Sqrt[3] Pi)) Pi)/Sqrt[3])

from some trial and error it seems the result is also incorrect for non-integer factors in the exponential.