LRiemann[f_, {a_, b_, n_}] := Module[
  {dx, i, c, rect, plot, sum},
  dx = N[(b - a)/n];
  c = Table[a + i*dx, {i, 0, n}];
  rect = Table[
    Rectangle[   {  c[[i]], 0}, {c[[i + 1]], f[c[[i]]]   }   ] ,  {i,
     1, n}         ];
    plot =
   Plot[f[x], {x, a, b}, AxesOrigin -> {0, 0},
    PlotLabel ->
     Style[f[x] sum "-> Aprox. Area of f(x) = ", FontSize -> 15],
    PlotRange -> All, PlotStyle -> Directive[Thick, Black]];
    sum = dx*Sum[f[a + (j - 1)*dx], {j, 1, n}];
  Show[
    plot,
    Graphics[{RGBColor[166/255, 206/255, 227/255],
     EdgeForm[Directive[Thin, RGBColor[31/255, 120/255, 180/255]]],
     Opacity[0.5], rect}]
    ]
    ]
f[x_] := x*Sin[x];
Animate[
 LRiemann[f, {-3 Pi, 3 Pi, n}] , {n, 1, 60},
 AnimationRunning -> False ]