Riemann Integral
The integral concept is associate to the concept of area. We began considering the area limited by the graph of a function and the x-axis between two vertical lines. This area can be aproximated using rectangles and the integral can be defined as the limit of the sum of the areas of the rectangles.
We can modify the function and the number of rectangles. In each interval, the height of the rectangle can be any value of the function in a point of the interval; here we consider only two simple possibilities.
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The error approximating the integral
When approximating an integral using rectangles we commit an error. In some cases, for example, in monotonic functions, we can limit the magnitude of the error.
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