Area-under-graph in a velocity-time graph tells us the

Displacement is proportional to square of time indicates that displacement increases linearly with square of time. 

As velocity is proportional to displacement, when displacement is varying linearly with time, velocity will also increase linearly with time, therefore, the acceleration will be uniform.

The area under the line on a velocity-time graph equals the object's displacement. If the graph's shape can be broken down into simple geometric shapes, the total area under the line can be calculated by adding the areas of those shapes together. The distance is represented by the area under a speed-time graph.