Inverse Laplace transform of two-sided and one-sided Laplace transform
The inversion formula is the same for both types of transforms:

$$f(t)=\frac{1}{2\pi j}\int_{\alpha-j\infty}^{\alpha+j\infty}F(s)e^{st}ds\tag{1}$$

The difference is in the choice of the constant $\alpha$. The line $\textrm{Re}\{s\}=\alpha$ must be inside the region of convergence (ROC). For causal functions (i.e., functions for which $f(t)=0$ for $t&lt;0$), the ROC is to the right of the pole with the most positive real part, whereas for non-causal functions, the ROC is a vertical strip between two poles.