I'm fine with calculating the work done when pumping water out of a tank. Set up the integral: $\int_{span\ of\ depth}\rho gh \ dV$
Where typically $h$ is the height to the surface of the water outside the tank and $dV=length \ dy$ Where the length can be rewritten as a function of y to follow the outside of your curve (since we're integrating with y).
I just have a conceptual question. This formula is assuming we are pumping water from the bottom of the tank.
Suppose we are to pump this water into another tank, and fill that tank bottom-up, would that make us calculate the work also done going into the second tank? $W_{total} = W_{emptying} + W_{filling}$ ?