Suppose that the life distribution of an item has hazard rate function $\lambda(t)=2.1 t^2, \ t>0$. What is the probability that
(a) the item survives to age $2$?
(b) the item's lifetime is between $1.5$ and $3$?
(c) a $0.5$-year-old item will survive to age $3.5$?