I am trying to compute the action of this graph if m = 1 then I assume that the Lagrangian is the integral of T-V = 1 - 0.5t^2 for 0 <= t < 1 and T = 1.5 - (.5 - 0.5t^2) for 1 < t <= 2.

This is assuming that T is the slope of the line squared and that V is mx and I'm basically absorbing g into the units for x as V is traditonally = mgh.

Does this look like I am approaching this in the right way? I am probably getting myself confused here as I am really not sure how to integrate this.