What is the relationship between work and potential energy?

[henpen]

If
Work= $\int$Fdx
and
Potential Energy, U= -$\int$Fdx

What is Work in terms of potential (and potential and kinetic) energy?
http://en.wikipedia.org/wiki/Potential_energy#Overview and http://en.wikipedia.org/wiki/Forms_of_energy#Potential_energy don't seem to agree on this. It seems odd that as work and potential energy seem so similar that W= -$\Delta$U

Also, why does Work= $\int$Fdx mean that, for a conservative force, F=grad(W)?

 

[Greg Bernhardt]

Potential energy is stored energy. It is the energy that an object possesses due to its position in a force field or due to its configuration. Potential energy is the energy that an object possesses due to its position in a force field or due to its configuration.