Eleven numerical methods for estimation of AUC (including 4 new methods) and 22 methods for AUMC (including 8 new methods) were tested on large simulated noisy datasets representing bolus, oral and infusion concentration-time profiles. Some methods were unacceptable because their mean error was large; these included a commonly recommended form of the linear trapezoidal rule for AUMC. Others, notably Lagrange and cubic spline methods, were unacceptable because the variance of their estimates was large. These methods should be abandoned. A simple and easily programmed new method, parabolas-through-the-origin then log-trapezoidal rule, performed especially well.