y=sin^2x+sinxcosx+2cos^2x
=sinxcosx+cos^2x+1
=(1/2)(sin2x+cos2x)+3/2
=(√2/2)sin(2x+45°)+3/2
∵-1≤sin(2x+45°)≤1
∴y∈[3/2-√2/2,3/2+√2/2]
即为所求