PDF[FRatioDistribution[m,n],x]

PDF[FRatioDistribution[5,42],x]

Manipulate[Plot[PDF[FRatioDistribution[m, n], x], {x, 0, 5}, PlotRange->{0,1}], {m,2,10,1}, {n,2,100,1}]

Manipulate[
Graphics[{
{Blue,Line[Table[{x,PDF[FRatioDistribution[m, n],x]},{x, 0, 5, .01}]],
Text["The F distribution with\nm = "<>ToString[m]<>" and n = "<>ToString[n]<>"  degrees of freedom", {3, .5}]}, 
{Red,
Polygon[ 
Join[
{{r,0}},
Table[{x,PDF[FRatioDistribution[m, n],x]},{x, r, 5, .01}], 
{{5,0}, {r,0}}]
],
Text["r = "<>ToString[r], {r, -.1}, {-1,0}],
Text["Red Area = "<>ToString[NIntegrate[PDF[FRatioDistribution[m, n],x], {x,r,Infinity}]], {3, .2}]
}
},
AspectRatio->.6,
Axes->True
],
{m,3,10,1},
{n,3,100,1},
{r,0,4}
]