F[x_]=Piecewise[{{1,-1<x<1}}]

Plot[F[x],{x,-10,10},AspectRatio->Automatic,Ticks->{Automatic,{1}},ImageSize->Large,PlotRange->All]

G[x_]=Exp[-x^2]

Plot[G[x],{x,-10,10},AspectRatio->Automatic,Ticks->{Automatic,{1}},PlotRange->All,ImageSize->Large]

Animate[Plot[F[x-t]+G[x+t],{x,-10,10},PlotRange->{0,2},AspectRatio->Automatic,
Ticks->{Automatic,{1,2}},ImageSize->Large,PlotStyle->Thick],{t,0,12},AnimationRunning->False,AnimationRate->1]