How do you calculate the distance travelled in a graph of irregular acceleration and irregular deceleration?

Assuming that the graph is continuous, you integrate to find the area under the curve. Judging by the nature of your question, and your additional info, you haven't studied calculus. If the graph is a straight line, then you can easily form a rectangle, or a triangle.

If the graph is a curve, then you can still form these rectangles, but they need to be much smaller. In fact, we make them infinitely small. Then we calculate the area of each rectangle and add them together.

This is what the definite integral is made to do. More.

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