∫x^2(six2x+x^2)dx=[∫x^2sin2xdx+x^4dx]|[-1,1].
=[(1/3)∫sin2xd(x^3)+∫x^4dx]|[-1,1]
={[(1/3)sin2x*x^3|[-1,1]-∫x^3(1/2)d(-cos2x)+(1/5)∫d(x^5)}|[-1,1].
={[(1/3)sin2x*x^3|[-1,1]+(1/2)cos2x*x^3|[-1,1]+(1/5)x^5|[-1,1].
=(1/3)sin2*1*(1)^3-(1/3)sin2*(-1)*(-1)^3+(1/2)cos2*1*(1^3)-(1/2)cos2*(-1)*(-1^3)+(1/5)[1^5-(-1^5)]
=(1/3)sin2-1/3sin2+(1/2)cos2+(1/2)cos2+2/5.
=2/5+cos2.