Can either of the below expressions involving an unknown analytic function $h(s,t)$ and the inverse Laplace transform $\mathcal{L}^{-1}$ be simplified? $$ \int\limits_{0}^1 \mathcal{L}^{-1} \left\{ \frac{h(s,t)}{s} \right\} \mathrm{d}t; $$
$$ \int\limits_{-\infty}^{\infty}\mathcal{L}^{-1} \left\{ \frac{h(s,t)}{s} \right\} \mathrm{d}t. $$