The area under a velocity-time graph gives the displacement. The velocity-time and acceleration-time graphs for common motions are shown below.

But if you calculate the acceleration without the graph, you are explicitly stating that the y-intercept is zero---which it might not be. So there are some actual reasons for making a graph.

Key fact The gradient of speed-time and velocity-time graphs represent acceleration. The area under a speed-time graph represents the distance travelled.