There certainly might be a better way of doing this, but does this give you enough of a hint that you can modify this to get what you are looking for?
Show[{
Plot[{Sin[x], Cos[x]}, {x, 0, Pi/4}, PlotRange -> {{0, 2 Pi}, {-1.01, 1}}],
Plot[{Sin[x], Cos[x]}, {x, Pi/4, 5 Pi/4}, Filling -> {1 -> {2}},
FillingStyle -> Yellow, AxesLabel -> {"x", "y"},
Ticks -> {{Pi/4, 5 Pi/4, 2 Pi}, {-1, 1}},
GridLines -> {{{Pi/4, {Red, Dashed,
Thickness[0.003]}}, {5 Pi/4, {Red, Dashed, Thickness[0.003]}},
2 Pi}, {-1, -Sqrt[2]/2, Sqrt[2]/2, 1}}],
Plot[{Sin[x], Cos[x]}, {x, 5 Pi/4, 2 Pi}]
}]
