Imagine a spring oriented vertically, with a particle attached to the end that is facing the ground. Take the axis to be oriented vertically. Why does the potential energy of this particle = mgx + .5kx^2 instead of mgx - .5kx^2? When I integrate the net force on the particle (mg-kx) times dx, from x naught to x, I get the answer mgx - .5kx^2.