On historical basis the problem that led to Definite Integral was the calculation of plane surfaces areas bounded by curvilinear edges. The method follows that used in elementary geometry for circle's area calculation. As first step we must consider a particular case. Let y(x) be a continuous and anywhere  positive function in (x1-x2) interval. The area bounded by curve, x axis and vertical segments in x1 and x2, is called TRAPEZOID (white zone).In order to calculate such an area we subdivide (x1-x2) interval in  some small identical intervals Dx, say n, so that Dx=(x2-x1)/n. In each of these we'll name m_i and M_i respectively the minimum and maximum value of the function in ith interval.