pi=Pi//N;
f[x_,t_]:=1/(2 c Sqrt[pi t]) Exp[-x^2/(4 c^2 t)];
c=0.5;u0[x_]:=If[x>2 && x<3,1,0];
u[x_,t_]:=If[t>0,NIntegrate[f[x-y,t],{y,2,3}],u0[x]];
bild=Plot3D[u[x,t],{x,1,4},{t,0,1},PlotPoints->30,PlotRange->All,
AxesLabel->{"x","t","u"},ImageSize->{400,300}];