y=2(1-cos^2x)+5cosx-1
=-2cos^2x+5cosx+1
=-2(cos^2x-5/2cosx-1/2)
=-2(cos^2x-5/2cosx+25/16-33/16)
=-2(cosx-5/4)^2+33/8
∵cosx∈[-1,1]
所以cosx-5/4∈[-9/4,-1/4]
y∈[-6,4]