Does Integration Imply Superposition in Field Calculations but Not in Energy?

[Kolahal Bhattacharya]

While calculating field and potential due to a continuous distribution of mass and charge,we use the standard methods of integration.Does it imply the validity of principle of superposition?If it does,then why we do not see it in the case of calculation of energy of the same distribution?

 

[neutrino]

The energy is proportional to the square of the field. Square of the sum is not always equal to sum of the squares.