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For example consider the following integration:

f(x) = x^3 [from 1 to 3]

$$\int_{1}^{3}x^{3}dx$$

when we subtract: {(3^4)/4}-{(1^4)/4}

why we get the result?

I meant to say, how we get the area by subtraction between upper and lower bounds of a function!

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    [(Very) related.](http://math.stackexchange.com/questions/15294)2011-05-01

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