This might be a silly question, but please help me understand that does the limits of the following expression. The left-hand-side is the actual expression, while the right-hand-side is my understanding.
$$\displaystyle \large e^{-\lambda\int_\mathbb{R^d}(1-e^{-f(x)})dx} = e^{-\lambda\int_x^\infty(1-e^{-f(x)})dx}$$
(We are dealing with a 2D euclidean plane here.)