Needs["Graphics`FilledPlot`"];
f[x_]:=0 /; x<1;
f[x_]:=0 /; x>3;
f[x_]:=x^2 /; x>=1 && x<=3;
bild=FilledPlot[f[x],{x,0,4},
Fills->GrayLevel[0.8],ImageSize->{400,300}];