The manufacturer of Cyrus' favorite top publishes a PDF for the length of time it takes the top, once spun, to stop spinning. The random variable giving the time to stop spinning is

T. This PDF is fT(t) = 0 if t<0,

1/((t+1)^2 if t>0 where t is measured in seconds.

1. Cyrus tells Luke that his top can spin for an hour straight. Luke suggests that while he's technically right, less than 0.1% of spins will last that long. Is Luke correct?
2. What is the closed form of CDF?