Using the Gain block to solve an integral equation

I'm starting to use Simulink and I have some doubts about using the blocks, if I'm going to integrate a function f (x) = x, I have a solution y (x) = (x^2)/2, using the Scope block it is possible see this, if the equation is f (x) = 4x, the solution will be y (x) = 2x^2.

For analogy, if I try to solve x '' = (1/m) F - (c/m) x '- (k/m)x, I cannot use the same idea, in the figure below I show better what I mean , in green the solution shown in several books and in red using as I understood it should be (and it's wrong) but I can't see why.

Thanks