Recreational math.

Can anyone solve this real quick? No complicated math required, only basic integration is required. It's little tricky tho.
[tex]\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin^2(x)}{1+e^x} ,dx[/tex]
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My progress:
[tex]\int{-\pi/2}^{\pi/2}\frac{sin^2x}{1+e^x} ,dx = \int{-\pi/2}^{\pi/2} \sin^2x (\frac{1}{1+e^x}-\frac{1}{2}+\frac{1}{2}) ,dx = \int_{-\pi/2}^{\pi/2} \frac{sin^2x}{2} ,dx[/tex]
I splitted the integral into two, one of which will be of an odd function so it will evaluate to 0..

(then, i became clueless!.. afterwards!) ​