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you dont have the means to calculate an area with a wobbly line on top. you do have the means to calculate an area as a sum of a looot of rectangles. so you put a lot of rectangles next to each other, each rectangle touching the wobbly line on top. putting more and more and more thin rectangles next to each other will give you a very, very, very good estimate of the area. calculating the limit will give you the exact area. thats Riemanns integral.
