Inverse Mellin Transform

Question

We all know that the Inverse Mellin Transform is $$\left\{\mathcal{M}^{-1}\varphi\right\}(x) = f(x)=\frac{1}{2 \pi i} \int_{c-i \infty}^{c+i \infty} x^{-s} \varphi(s)\, \mathrm{d}s.$$ So what is my problem? I want to calculate an integral, which looks like: $$\frac{1}{2 \pi i} \int_{c-i \infty}^{c+i \infty} x^{s} \varphi(s)\, \mathrm{d}s$$ I want to express this integral as a Inverse Mellin Transformation. My idea was to do a small substitution, so that $s \rightarrow -s$. But then the integral has different boundaries: $$-\frac{1}{2 \pi i} \int_{-c+i \infty}^{-c-i \infty} x^{-s} \varphi(s)\, \mathrm{d}s = \frac{1}{2 \pi i} \int_{-c-i \infty}^{-c+i \infty} x^{-s} \varphi(s)\, \mathrm{d}s$$ This is an Inverse Mellin Transform but $c\rightarrow-c$. How can I get to a real Inverse Mellin Transform?