Sound absorption across a wide range of frequencies is a focus in contemporary acoustics. Recently, integral bounds of absorption or reflection coefficients were introduced as a guide of design optimization following the footsteps of electromagnetics, where integral relations were derived based on system causality considerations. This talk carefully examines the proper formulation of physical causality and its implications on the scattering properties of the system. Taking into consideration the effects of different physical boundary conditions and the bulk absorber material, a more generalized integral bound is derived. It becomes evident that, while the bound exists, it is governed by system stiffness rather than the causality constraint. By studying the effects of various approximations made during mathematical derivations, the physics of the bound is thoroughly discussed, and the limitations in utilizing integral bounds as reference for design optimization are highlighted. The findings are expected to have significant implications for the development of effective noise reduction strategies and the advancement of smart acoustic design.