Let’s assume that is continuous and positive on the interval . Then the definite integral represents the area of the region bounded by the graph of and the x-axis, from x = a to x = b. First, we partition the interval into n subintervals, each of width such that Then we can form a trapezoid for each subinterval and the area of the ith trapezoid = . This implies that the sum of the areas of the n trapezoids is Area =