The discussion revolves around a challenging integration problem involving the expression Int(from 0 to x) (1-F(x-t)) dF(x). The user expresses confusion about calculating the integral, particularly when needing to derive results within F(x) without knowing the density function. Clarifications are made regarding the integration with respect to different variables and the implications of convolution in the context of distribution functions. Ultimately, the user finds the solution in their stochastic scriptum, revealing that for independent random variables x and y with distribution functions F and G, the distribution of their sum can be expressed as H(a)=P(x+y<=a)=int F(a-v)dG(v). This highlights the connection between integration and probability distributions in the context of random variables.