Facts you should know
i also did by parts on the last integral also, but it never seemed to be leading me anywhere. and even if i could get a nice result, i'm not exactly sure how you expect me to combine the two integrals when they have different variables.
I plugged the integral in on my calculator and got that
At a glance it looked like an integration by parts, but I guess it isn't. (Or, rather, it still may be but I can't figure how to do it.) I'll have to work on the integral a bit, but in any event you should be able to see where to go with it from here.
Edit: Ah wait! I see where Krizalid is going with this. The integrand isn't an even function, but the two are reflections of each other over the y-axis. Since the integration limits are symmetric the two integrals must be equal to each other.