I have a question concerning These two similar sets:
\begin{align\*}
A&=\{(s,y)\in\mathbb{R}\_+ \times \mathbb{R}\_+:s+y\leq t\}\\
B&=\{(w,z)\in\mathbb{R} \times \mathbb{R}:w+z\leq t\}\\
\end{align\*}
I found two integral over each of these sets. 

$$I(B) = \int\_{-\infty}^\infty \int\_{-\infty}^{t-z} f(w,z) \mathrm{d}w \mathrm{d}z$$
and
$$I(A)=\int\_{0}^t \int\_{0}^{t-s} f(s,y) \mathrm{d}y \mathrm{d}s$$

But why is the outer integral different? Why is it not
$$I(A)=\int\_{0}^\infty \int\_{0}^{t-s} f(s,y) \mathrm{d}y \mathrm{d}s$$

I don't understand this. Or is one wrong?