y=-2sin²x+2sinx+1=-2(sinx²-sinx+1/4)+3/2
=-2(sinx-1/2)²+3/2
∵sinx∈[-1,1]
∴当x=1/2时,y取最大值3/2
当x=-1时,y取最小值-3
∴y∈[-3,3/2]