Hazard Rate Function?

I am trying to do the following question:

The lifetime X (in years) of an item has a rate function $λX(t) = t^2 + t^4 \,for\, t > 0$. What is the probability that
a) an item survives to age 1?
b) an item’s lifetime is between .5 and 1.5?
c) a 1/2 year old item will survive to age 1?
d) Now suppose the rate has doubled and let Y be the new lifetime with respect to the rate function $2\lambda_{X}(t)$.
What is $P(Y > 1|Y > .5)$?

I'm not sure how to tackle this question. In my book it says that the hazard rate function is defined by $\lambda(t)=\frac{f(t)}{\bar F(t)} \, where \bar F = 1 - F$ but the rate function we are given isn't similar to this form? I suppose I'm suppose to use the rate function in the exponential distribution. The book gives a very small explanation about hazard rate functions, and only one example so I'm having a hard time understand it. Please help!