I defined a function of two variables, let's say
u[x_, y_] := 4 x^4 + 6 x y - 24 x^2 y^2 + 4 y^4
I want to partial integrate (with respect to y) the partial derivative of u with respect to x obtaining a function v[x_,y_] in which is present an additive function of x, let's say c[x]. I tried
v[x_, y_] = Integrate[\!\( \*SubscriptBox[\(\[PartialD]\), \(x\)]\ \(u[x, y]\)\), y, GeneratedParameters -> C]
but so I obtain a constant function c_1. Otherwise I have to add to the integral c[x]. Is it possible to obtain an additive function of x with GeneratedParameters?