Fitting a parabola to four Cartesian points - Part 2 -

In the Cartesian $xy$ -plane, you are given the following four points, $A (5, 0), B(1, -1), C(-3, 5) , D(6, 4)$ . You want to fit a parabola that will pass through the four points. As it turns out, there are two such parabolas shown in the figure below in blue and green colors. Find the two fitting parabolas to the four given points, and find the area $A$ of the region that is bounded by branches of the two parabolas, indicated in the figure below by the shaded region. Enter the value of $\lfloor 10^4 A \rfloor$ as your answer. The figure is drawn to scale.