y=cos²x+sinx
=1-sin²x+sinx
=-(sinx-1/2)²+5/4
因为x∈[-π/4,π/4]
所以sinx∈[-√2/2,√2/2]
所以最大值是-(1/2-1/2)²+5/4=5/4最小值是-(-√2/2-1/2)²+5/4=(1-√2)/2