Clear[i, sigma, n, mu, g]

g[ x_] = (1/(Sqrt[ 2 Pi n] sigma)) E^( -(x - n mu)^2/(2 n sigma^2))

i = Integrate[ g[x], {x, -Infinity, Infinity}] ;
Simplify[ i, sigma > 0 && n > 0 && mu > 0]