Given a stream of rectangles over a discrete space, we consider the problem of computing the total number of distinct points covered by the rectangles. This can be seen as the discrete version of the two-dimensional Klee's measure problem for streaming inputs. We provide an (epsilon, delta)- approximation for fat rectangles. For the case of arbitrary rectangles, we provide an O(sqrt{log U})-approximation, where U is the total number of discrete points in the two-dimensional space. The time to process each rectangle, the total required space, and the time to answer a query for the total area is polylogarithmic in U. Our approximations are based on an efficient transformation technique which projects rectangle areas to one-dimensional ranges, and then uses an F_0 streaming algorithm in the one-dimensional space. The projection is deterministic and to our knowledge it is the first approach of this kind which provides efficiency and accuracy trade-offs in the streaming model.