F(x)=cos^2x+sinx
=1-sin^2x+sinx
sinx=t -1/√2≤t≤1/√2
F(t)=1-t^2+t=-t^2+t-1/4+5/4=-(t-1/2)^2+5/4
F(t)开口向下,对称轴 t =1/2
t= -1/√2时,函数F(t)有最小值
最小值 1-1/2-1/√2=1/2-1/√2