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I should Show the following:

D is subset of R^2 with the triangle (0,0),(1,0),(0,1). g is steady.

Integral_D g(x+y) dL^2(x,y)=Integral_0^1 g(t)*t*dt

my ansatz:

Integral_0^1(Integral_0^(1-x) g(x+y) dy) dx

With Substitution t=x+y

Integral_0^1(Integral_x^1 g(t) dt) dx

But now i dont Have any ideas how to go on:-(