Question
Acceleration is calculated from $v - t$ graph while is area under $v - t$ graph.

Answer

Acceleration is calculated from $v - t$ graph while Displacement is area under $v - t$ graph.
Explanation:
The area under a velocity-time graph is a representation of the displacement. If the area is over a time interval, then the displacement during that time interval can be measured by the area under the graph bounded by the time interval.
Bonus: the slope of a $V - t$ graph is a measure of acceleration.

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