Minimizing Area

Source: The second problem in this video.

There is a rectangle and a path that goes from the bottom-left corner to the top-right. The path can only move upwards or towards the right. Draw a vertical line $L$ through the rectangle. Now look at the area under the curve to the left of $L$, and the area above the curve to the right of $L$. Call this total area $A_L$. In the example figure below, $L$ is the dotted line and $A_L$ is the shaded area.

Area associated with the path and a line $L$.

What is the line $L$ that minimizes $A_L$?