Summary: We make certain continuity and disconjugacy assumptions upon the second-order boundary value problem with nonlocal integral boundary conditions, \[ \begin{gathered} y''= f(x,y,y'),\quad y(x_1)= y_1,\;\text{and}\\ y(x_2)+ \int^d_c ry(x)\,dx,\;a< x_1< c< d< x_2< b,\;y_1,y_2,\;r\in\mathbb{R}.\end{gathered} \] Then, supposing we have a solution, \(y(x)\), of the boundary value problem, we differentiate the solution with respect to various boundary parameters. We show that the resulting function solves the associated variational equation of \(y(x)\).