Finding the Area Under a Curve with Integration

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Here is part 2 of my area calculations. In this method, I show that an integral is an anti derivative. Using this, I find the area under the function f(x) = 3x^2 +2 from 1 to 2.

Here is part 1 in which I do the same thing but with summation notation.
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This man just proved the fundamental theorem of calculus with pictures. I'm calling the real analysis police.

cauchyscouch