Standard way of finding a inverse Laplace transform

35 Views Asked by At

Is there a standard procedure to find this inverse Laplace transform? $$\mathcal{L}_t\left[\int_\text{a}^\text{b}f(t)e^{-\text{s}t}\space\text{d}t\right]_{\left(\text{s}\right)}=\dots\tag1$$

Where $\text{a}$ and $\text{b}$ are real and positive.