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Calculus question (do not know much about calculus)

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What does finding the area under a curve actually mean in different cases? Like I know what you do, but what is its implication in different real-world scenarios. For example, it can be used to find velocity and stuff but is there other useful applications. I've been trying to think of topics for my Math IA but it is hard because I don't know much about the course content as we have only learned probability so far.

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There's an application in economics called the Gini coefficient - there is basically a curve called the Lorenz Curve and a line called line of equality in a square plane (look it up for an image, which would be clearer). For the Gini coefficient, find the area under the line of equality (should look like a triangle). Then find the area between the Lorenz Curve and the line. Divide the second are by the first and the answer is the Gini coefficient. 

I'd warn you that the math is kind of hard, there's no 'equation' as such for the Lorenz Curve so you will have to go into another method. 

That's one application, though! Hope it helps and look up the diagram to get a better picture of it. 

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