(sinx+cosx)^2=(sinx)^2+(cosx)^2+2sinxcosx=1+2sinxcosx
所以2sinxcosx=(sinx+cosx)^2-1
令a=sinx+cosx=√2sin(x+π/4)
所以-√2<=a<=√2
则y=a+(a^2-1)+2=a^2+a+1=(a+1/2)^2+3/4
-√2<=a<=√2
所以a=-1/2,y最小=3/4
a=√2,y最大=3+√2
所以值域[3/4,3+√2]