Why does adding a dielectric increase the energy of a capacitor?

[alexio]

First of all, I am not a native speaker so the sentence I wrote may not make sense.
So If you want to know meaning of it pleask ask me.
In most of the nature phenomena, most thing has been happened to reduce there potential or energy.
However if insert a dielectric in the gap of a capacitor, it is automatically happen because of the attraction between the dielectric and the capacitor even though it makes the energy of the capacitor higher. Why is it happen? I want to know it.

 

[Meir Achuz]

In the case of constant voiltage, the battery keeping V constant does work, so the energy of the capacitor is increased as the dielectric moves in.