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At its core, the idea of integration is about combing small pieces to form the bigger picture. This concept is typically introduced by considering how to compute the area of an oddly shaped region by combing (integrating) the areas of rectangular regions. These summations are commonly knowns as Riemann sums.
If \(f(x)\) is integrable on the interval \([a,b]\) then
\(\displaystyle\int_{a}^{b}f(x)dx = \underset{n\to\infty}{\lim}\sum_{k=1}^n f(x_k)\Delta x\)
where \(x_k=a+k\Delta x\) and \(\displaystyle\Delta x=\frac{b-a}{n}\)
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