I am seeing a derivation which I do not understand totally. I would appreciate if someone could help me out.
Let $f(t)$ specify the event probability at moment $t$. Further, assume that $P(1)$ denotes the probability of one event occurring during time $T$ and $P(2)$ denotes the probability that two events occur during time $T$.
$P(1) = \int_{0}^{T}f(t)dt$
$P(2) = \int_{t2}^{T}(\int_{0}^{t2}f(t_1)dt_1)dt_2 = \frac{1}{2}(2*\int_{t2}^{T}(\int_{0}^{t2}f(t_1)dt_1)dt_2 = \frac{1}{2}(\int_{0}^{T}f(t)dt)^2 = \frac{1}{2}P(1)^2$
How were the double integrals converted in the final step?