Expected value of uniform distribution

Theorem

Let $X$ have the uniform distribution on $[a,b] \cap \mathbb{T}$. Then, $$\mathrm{E}_{\mathbb{T}}(X) = \dfrac{h_2(\sigma(b),a)}{\sigma(b)-a}+a,$$ where $h_2$ denotes the delta hk and $\sigma$ denotes the forward jump.