A Riemann ("ree-mahn") sum is a mathematical technique for approximating the area under a function or curve, named after the German mathematician Georg Friedrich Bernhard Riemann. The technique involves estimating the area under a function by splitting it into variably sized rectangles whose areas can easily be found. Riemann sums are important to Calculus since they are the precursors to definite integrals or antiderivatives, which are really just Riemann sums made acurate by narrowing the rectangles to an infinitely small width. Riemann sums are taken relative to the x-axis, and areas between a function below the x-axis and the x-axis are considered positive.