When the upper and lower limits are the same but the only difference being their signs, you have to use this property:
Replace x by -x.
If f(-x) = -f(x) [That means it is an odd function] = > It's integral is zero.
if f(-x) = f(x) [an even function], you have to multiply the integral by 2 and replace the lower limit by 0.
In the question, if you observe, you would multiply sin^4x inside the bracket. The first function you would get is an even function and the second one is an odd function, then you integrate them separately. From there, it is very simple.