ClearAll;
g[x_]:= x^2 (2-x)^2;
L = 2 Integrate[g[x],{x,0,1}];
f[x_]:= g[x]/L;
mu = 1;
sigmasq = 2 Integrate[(x-mu)^2 f[x],{x,0,1}];
kappa = Sqrt[sigmasq]/mu;
sigmasq
kappa