Assuming that $\int_{-\infty}^{+\infty} \exp\left(-x^{2}\right) \mathrm{d}x = \sqrt{\pi}$, give the value of $\int_{-\infty}^{+\infty} g_{\sigma}(x) \mathrm{d}x$.
Assuming that $\int_{-\infty}^{+\infty} \exp\left(-x^{2}\right) \mathrm{d}x = \sqrt{\pi}$, give the value of $\int_{-\infty}^{+\infty} g_{\sigma}(x) \mathrm{d}x$.