dear professor,
Why do text books always leave the EPV of an n year life insurance benefit of one unit of money payable at the instant of death as the integral with respect to t between 0 and n of the function e^(-delta*t)*t_p_x*mu_x+t and not show that, integrating by parts, this becomes one minus e^(-delta*n)*n_p_x minus the integral with respect to t between 0 and n of the function delta* e^(-delta*t)*t_p_x