Clear[F]

F[a_] := 
      Plot[Exp[-2*x], {x, 0, a}, PlotStyle -> Hue[0.0], 
        AspectRatio -> Automatic, PlotRange -> {0, 1}]

F[2]

Show[G[3, 2], F[2]]

Show[G[4, 2], F[2]]

Show[G[10, 2], F[2]]

Show[G[20, 2], 
      F[2]]

Show[G[100, 2], F[2]]

Clear[Anime]

Anime[a_, k_, m_] := Do[Show[G[n, a], F[a]], {n, k, m, 3}]

Anime[2, 3, 18]