Here's why:

* Velocity is the rate of change of displacement.

* Area under a curve represents the product of the two quantities represented on the axes.

* Therefore, the area under a velocity-time graph represents the product of velocity and time, which is displacement.

Example:

Imagine a car moving at a constant velocity of 10 m/s for 5 seconds. The velocity-time graph would be a horizontal line at 10 m/s. The area under the curve is a rectangle with a height of 10 m/s and a width of 5 seconds. The area (and displacement) is 10 m/s * 5 s = 50 meters.