You can get the value of the area of a given function F (x) in interval [a, b] adding to the areas of rectangles defined by the curve of the function, is adopting a width D of rectangles as small as you want. It begins assuming D = (b-a) / 2, and repeatedly, as is D = D / 2, calculated at the sum of A1 and A2 areas of contiguous rectangles alternate in x and x + D, respectively, given by A1 = abs (f (x)) * D and A2 = abs (f (x + D)) * D, throughout the interval, until the absolute difference of the two areas is less than one and arbitrary. The end value of area is A1 + A2.
a) Describe it in terms of its elements: input, output and terms of the result.
b) Make the examination of the above in terms of problems and subproblemas, using the technique of successive refinements.