Brain Teaser - Area enclosed by a parabola and a line

[Bunuel66]

Case x<0

If one understands the question as related to a positive area, it seems that:

h(x) becomes simply -h(x) for x<0 with the same minimum for x=-0.5

Seems to be reasonable as the problem has an axial symmetry relative to y.

Then the general solution would be just abs(h(x)) as the sign of h(x) is the same as the one of x.

Regards.