I'm not sure how robust this is. It is quick and dirty so to speak.

With[{abbrev := Sum[int[i], {i, 1, n$}]}, f[n_] := abbrev + y; g[n_] := abbrev^2 (*and so on*)] 

...but I think @kuba's link provides better alternatives

I'm not sure how robust this is. It is quick and dirty so to speak.

With[{abbrev := Sum[int[i], {i, 1, n$}]}, f[n_] := abbrev + y; g[n_] := abbrev^2 (*and so on*)] 

...but I think @kuba's link provides better alternatives.

Edit

Such an alternative includes:

Clear[f, g]; Module[{abbrev := Sum[int[i], {i, 1, n}]}, SetDelayed @@ {f[n_], abbrev + y}; g[n_] := abbrev^2] 

Where you do not have to modify the n with dollar signs. The explanation for why this works is given in the post by Mr Wizard and Leonid.