Plot Filling restricted to domain segment

One Plot can do too:

Plot[{If[x < 1, 1/(x^2)], If[x > 1, 1/(x^2)]}, {x, 0, 4}
 , AspectRatio -> 1
 , Filling -> {2 -> {Axis, Red}}
 , Epilog -> {Purple, Rectangle[]}
]

Show[Plot[1/(x^2), {x, 0, 4}, PlotStyle -> Blue, AspectRatio -> 1],
 Plot[1, {x, 0, 1}, FillingStyle -> Purple, Filling -> Bottom, 
  PlotStyle -> Blue], 
 Plot[1/(x^2), {x, 1, 4}, PlotStyle -> Blue, Filling -> Axis, 
  FillingStyle -> Red, PlotRange -> {Full, {0, 1}}]]

Another variation, using ConditionalExpression:

Plot[{
  ConditionalExpression[x^-2, x <= 1],
  ConditionalExpression[x^-2, x > 1],
  ConditionalExpression[1, x <= 1]}
 , {x, 0, 4}, PlotStyle -> Blue,
 Filling -> {2 -> {Axis, Red}, 3 -> {Axis, Purple}}]