g1[x_] = x/2; g2[x_]:= 3 - x;
L = Integrate[g1[x],{x,0,2}] + Integrate[g2[x],{x,2,3}];
f1[x_] = g1[x]/L; f2[x_]:= g2[x]/L;
mu = Integrate[x f1[x],{x,0,2}] + Integrate[x f2[x],{x,2,3}];
sigmasq = Integrate[x^2 f1[x],{x,0,2}] + Integrate[x^2 f2[x],{x,2,3}] - mu^2;
kappa = Sqrt[sigmasq]/mu;
F1[t_] = Integrate[f1[x],{x,0,t}];
F2[t_] = F1[2] + Integrate[f2[x],{x,2,t}];
M = t/.Solve[F1[t]==1/2,t][[2]];
L
mu
sigmasq
kappa
F1[t]
F2[t]
M