Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 74, pp. 1-10. Title: Young's integral inequality with upper and lower bounds Authors: Douglas R. Anderson (Concordia College, Moorhead, MN, USA) Steven Noren (Concordia College, Moorhead, MN, USA) Brent Perreault (Concordia College, Moorhead, MN, USA) Submitted February 14, 2011. Published June 15, 2011. Math Subject Classifications: 26D15, 39A12, 34N05. Key Words: Young's inequality; monotone functions; Pochhammer lower factorial; difference equations; time scales.