## Washing Machine Hazard Rate Problem

The problem statement, all variables and given/known data
The number of years that a washing machine functions is a random variable whose hazard rate function, h(t), is given by

- 0.2 if 0 < t < 2
- 0.2 + 0.3(t - 2) if 2 <= t <= 5
- 1.1 if t > 5

If the washing machine is still working six years after being purchased, what is the conditional probability that it will fail within the succeeding two years?

The attempt at a solution
My interpretation of h(t) is that it is the probability that the washing machine will fail given that it has worked for t years.

The answer to the problem, I reckon, is the sum of h(6 + t) as t varies from 0 to 2. Since 6 + t > 5, then h(6 + t) = 1.1 by the def. of h. Integrating, I get 2.2. This must be wrong since probabilities are <= 1. Where did I go wrong?
 The solution in the book states that the answer is P{X < 8|X > 6}. What is X here? I guess it represents the number of years the washing machine has survived. This makes sense. Why didn't my original idea work? It seems perfectly legit. to me.