Time-integrated fluorescence cumulant analysis (TIFCA) is a data analysis technique for fluorescence fluctuation spectroscopy (FFS) that extracts information from the cumulants of the integrated fluorescence intensity. It is the first exact theory that describes the effect of sampling time on FFS experiment. Rebinning of data to longer sampling times helps to increase the signal/noise ratio of the experimental cumulants of the photon counts. The sampling time dependence of the cumulants encodes both brightness and diffusion information of the sample. TIFCA analysis extracts this information by fitting the cumulants to model functions. Generalization of TIFCA to multicolor FFS experiment is straightforward. Here, we present an overview of the theory, its implementation, as well as the benefits and requirements of TIFCA. The questions of why, when, and how to use TIFCA will be discussed. We give several examples of practical applications of TIFCA, particularly focused on measuring molecular interaction in living cells.