|x|<=π/3
则-π/3<=x<=π/3
-√3/2<=sinx<=√3/2
y=cos^2x+sinx+1
=1-sin^2x+sinx+1
=-(sin^2x-sinx+1/4)+1/4+2
=-(sinx-1/2)^2+9/4
sinx=-√3/2时,Ymin=-1-√3/2+9/4=5/4-√3/2
sinx=1/2时,Ymax=9/4
所以,所求值域：
5/4-√3/2<=y<=9/4