f(x)=-(sinx)^2-cosx=(cosx)^2-cosx-1=(cosx-1/2)^2-5/4
因x∈[π/2,3π/2],cosx∈[-1,0]
当cosx=0,f(x)最小值=(0-1/2)^2-5/4=-1
当cosx=-1,f(x)最大值=(-1-1/2)^2-5/4=1