Integral of a non-function?

\(y=y^z+x^z\)

I wanna take the definite integral of that relation but I guess I am not sure of the notation or if it is even possible...and from x(or/and y?) = -1 to 1

Z is just some abratrary value greater than 1...

 

I do not want \(\int_{-1}^{1} \int_{-1}^{1} y^z+x^z dydx\)

It is a graph on \(R^2\)

 

So yeah.... wondering if there is some kind of trick or what... or if the domain of the integral is simply limited to functions