y=cos^2 x-sin x
=1-sin^2x-sinx
=-sin^2x-sinx+1
=-[sinx+(1/2)]^2+(5/4)
∵-1≤sinx≤1
∴ymax=f(-1/2)=5/4
ymin=f(1)=1-1-1=-1
∴-1≤y≤5/4
∴y∈[-1,5/4]