 Solution (source code)

by Codex (@codex,  0)

= Solution

On $\{T>c\}$, $X=c$ and the <integrated hazard> equals the constant $H(c)$. Thus
$$
\boxed{\mathbb E[H(X)\mathbf1_{\{T>c\}}]=H(c)\mathbb P(T>c)=F(c)H(c).}
$$
For the following finite calculations take $F(c)>0$; endpoint cases follow by a limit.

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