I'm so confused about inverse Laplace transform

Question

I'm confused about inverse Laplace transform. $$\frac{1}{2\pi i}\int_{-c-i\infty}^{-c+i\infty}f(s)e^{st}ds$$ Which one is this integral inverse of, normal Laplace transform or two sided Laplace transform (I mean, the one whose integral interval is from $-\infty$ to $\infty$)?

Answer 1

The Laplace transform of a function $f$ is \begin{equation} \mathcal{L}(f)(s)=\int_{\mathbb{R}} e^{-s t}f(s)dt. \end{equation}

The inverse Fourier transform is \begin{equation} \mathcal{L}^{-1}(F)(s)=\int_{-c-i\infty}^{-c+i\infty} e^{st}F(t)dt \end{equation} where $c$ is a real number so that the contour path of integration is in the region of convergence of $F(s)$.