The closed-form solution for assessing the proportion of the mean annual frequency of limit-state exceedance as a function of integration limits is introduced, in order to study whether or not the mean annual frequency of limit-state exceedance is overestimated if the lower and(or) upper integration limit of the risk equation are(is) not selected in a physically consistent manner. Simple formulas for assessing the threshold value of the lower and upper integration limits are also derived. These formulas can be used to quickly assess the significant range of ground motion intensity that affects the mean annual frequency of limit-state exceedance. It is shown that the threshold values of the integration limits depend on the median intensity causing a limit-state, the corresponding dispersion and the slope of the hazard curve in the log domain. For several reinforced concrete buildings located in a region with moderate seismicity, it is demonstrated that the mean annual frequency of collapse can be significantly overestimated when assessed by integrating the risk equation over the entire range of ground motion intensity. Copyright © 2013 John Wiley & Sons, Ltd.