  We prove mean curvature and volume comparison estimates on smooth metric
measure spaces when their integral Bakry-\'{E}mery Ricci tensor bounds,
extending Wei-Wylie's comparison results to the integral case. We also apply
comparison results to get diameter estimates, eigenvalue estimates and volume
growth estimates on smooth metric measure spaces with their normalized integral
smallness for Bakry-\'{E}mery Ricci tensor. These give generalizations of some
work of Petersen-Wei, Aubry, Petersen-Sprouse, Yau and more.
