u1[x_] := 
      If[(x + t ≥ 0 && x - t ≤ 0), 1, 
        0]

Table[
      Plot[u1[x], {x, -20, 20}, 
        PlotStyle -> {RGBColor[1, 0.7, 0], Thickness[0.015]}, 
        PlotRange -> {{-20, 20}, {-1.1, 1.1}}], {t, 0, 12, 
        0.1}]