Hazard rate functions -- basic

Hi all,
I have two questions and would really appreciate it if someone help me
understand.

1. From the description about hazard rate function (A first course in
probability, by Sheldon Ross, p 215), I ran into the following
statements.

"Suppose now that the lifetime distribution is exponential. Then, by
the memoryless property, it follows that the distribution of remaining
life for a t-year-old item is the same as for a new item."

I am wondering what the "memoryless property" means. Also, is this
property limitted to exponential distribution?

2. (from the same book, p. 216)

lambda(t) = {d/dt(F(t))}/{1-F(t)}

where, lambda(t) ; hazard rate function, F(t); life time distribution
function
Integrating both sides yields,

log(1-F(t)) = - integral (lambda(t)) + k ; k = constant

Would someone explain to me how integration yields the above eqaution.


Thank you very much.

Jong-Hoon

.