To find the area under the graph of a functionffromatob, we divide the interval [a,b] intonsubintervals, all having the same length (b-a)/n. Observe the figure below.

Since f is continuous on each subinterval, f takes on a minimum value at some number c_i in each subinterval.
On can construct a rectangle with one side of length [x_{i - 1}, x_i], and the other side of length equal to the minimum distance f(c_i) from the x-axis to the graph of f.
The area of this rectangle is f(c_i) ¤x, where ¤x is (b - a)/n. The boundary of the region formed by the sum of these rectangles is called the inscribed rectangular polygon.
The area (A) under the graph of f from a to b follows below. Note that the summation sign Sigma is not an html character and will be denoted by £.
             _n
A = lim £ f(c_i) ¤x,      x_{i - 1} < c_i < x_i, where ¤x = (b - a)/n.
^{n-->infinity i = 1}
The area A under the graph may also be obtained by means of circumscribed rectangular polygons. In the case of the circumscribed polygons the maximum value of f on the interval [x_{i - 1}, x_i] is used.
Remember that the area obtained using circumscribed polygons should always be larger than that obtained by using inscribed rectangular polygons.