The curve intersects the $x-$axis at the points $(p,0),(q,0)$ and $(r,0),$ and region $U$ is the region enclosed by the curve and the $x-$axis between $x=p$ and $x=q.$

Given that the areas of regions $S$ and $U$ are equal, calculate the total area enclosed by the two curves in the first diagram. Be sure to provide a suitable justification for your answer.