The Arc drawing tool 
lets you make curvilinear polygons for which you can assign fill properties and find areas. There are some limitations, however. Since you can't construct a point on two intersecting curves (except for circles), you have to connect curves with line segments. If you want to connect two arcs, you have to first connect them with a line and move it to the intersection like this:
To make a curvilinear polygon of the intersecting parabolas here are the steps:
- Attach two lines.
- Make endpoints C and D -t point proportional along the curves.
- Make endpoints A and B t point proportional along the curves.
- Draw the two arcs - select Draw / Arc, from C to A and D to B.
- Select the sides and arcs of the polygon in order and click Construct / Polygon.
- Set t=2 in the Variables toolbox and the lines will become the intersection points.
It's easier with circles because you can place points on their intersections:
