The upper Riemann integral for a real-valued function f (x ) on an interval is computed to be the infimum of all finite sums over all partitions of the interval, the sums having terms given by (x_i - x_i-1)y_i , where the x_i are from a partition, and y_i is the largest value of f (x ) over the interval from x_i-1 to x_i .