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Mathematical portrait problem
f(x)=-x^2+x+ 1=-(x- 1/2)^2+5/4?

According to the image, the symmetry axis of the function is x= 1/2.

On [- 1, 1/2], the function is an increasing function with the range of [- 1, 5/4].

On [1/2, 1], this function is a decreasing function with the range of [1, 5/4].

∴ On [- 1, 1], the function range is [- 1, 5/4].

X∈[- 1, 1] does not exist, so f(x)=-2.