# 5.2 The Definite Integral

 In the previous section, we saw that if f is continuous on an interval [a,b], then the endpoint and midpoint approximations approach a common limit L as N → ∞: L = limN → ∞ RN = limN → ∞ LN = limN → ∞ MN When f(x) ≥ 0, L is the _____ under the graph of f. In a moment, we will state formally that L  is the _____ _______ of f over [a,b]. Before doing so, we introduce more general approximations called ______ _____ areadefinite integral Riemann sums Recall that RN, LN and MN use rectangles of equal width Δx, whose heights are the values of ____ at the endpoints or midpoints of the _______. In Riemann sum approximations, we relax these requirements: The rectangles need not have _____ width and height may be any value of ____ within the subinterval f(x)subintervalsequalf(x) To specify a Riemann sum, we choose a partion and a set of sample points (Define both) Partion: P of size N, a choice of points that divides [a,b] into N subintervals P: a = x0 < x1 < x2 <...