The definite integral, in the examples seen, represents an area, which occurs in many cases, and is one way of presenting the definite integral.

In general, for , the area limited by f (x) and the x axis, is given by , which can represent the sum of the areas of infinite rectangles in width and whose height is the value of the function at a point in the base range:

Subdividing the range a, b into **no **subintervals through abscissa x_{0}= a, x_{1}, x_{2},…, X_{no}= b, we get the intervals (a, x_{1}), (x_{1}, x_{2}),…, (X_{n-1}, B). At each interval (x_{i-1}, x_{i}) let's take an arbitrary point **H _{i}**

_{.}

Be According to the figure, the formed rectangles have an area

So the sum of the areas of all rectangles is:

which gives us an approximate value of the area considered.

Increasing the number **no** of subintervals such that zero is the number **no** from subintervals tent to infinity , we have the upper bases of the rectangles and the curve practically merging, so we have the area considered.

Symbolically, we write: