y=-t²+t+1
=-(t²-t+1/4-1/4)+1
=-(t-1/2)²+1/4+1
=-(t-1/2)²+5/4
(t-1/2)²≥0
-(t-1/2)²≤0
当t=1/2时,取得最大值5/4.
所以值域:(-无穷大,5/4]