This paper presents an algorithm for computing quantities involving integration of NURBS curves, such as areas, volumes of revolution, first moments of area, centroids etc., of regions bounded by plane NURBS curves. For quadratic NURBS curves,closed form integral solutions are derived, thus all integral values can be directly obtaind by the coordinates of control points and weights without approximation error. For cubic NURBS curves, an approximation method is given, which provides a simple error bound and has a speed advantage for small tolerance.