How to compute the limiting distribution of excess life, with uniform density?

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I'm working on the reward/renewal process question and get stuck in the following question.

could anyone please lend me some help?

-- Question:

What is the limiting distribution of excess life, when renewal lifetimes have the uniform density $f(x) = 1$, for $0<x<1$.

I know the answer is $h(x)=2(1-x)$, but I don't know how this answer came up.