PDF[StudentTDistribution[n],x]

PDF[StudentTDistribution[7],x]

Manipulate[Plot[{PDF[NormalDistribution[0,1],x],PDF[StudentTDistribution[n],x]},{x, -5, 5}, PlotStyle->{Blue, Green}], {n, 1, 16,1}]

Manipulate[
Graphics[{
{Blue,Line[Table[{x,PDF[NormalDistribution[0,1],x]},{x, -4, 4, .01}]]},
{Green,Line[Table[{x,PDF[StudentTDistribution[n],x]},{x, -4, 4, .01}]],
Text["Student's T distribution with\nn = "<>ToString[n]<>" degrees of freedom", {2.5, .35}]}, 
{Red,Opacity[.5],
Polygon[
Join[
{{r,0}},
Table[{x,PDF[StudentTDistribution[n],x]},{x, r, 4, .01}], 
{{4,0}, {r,0}}]
],
Text["r = "<>ToString[r], {r, -.05}, {-1,0}],
Text["Red Area = "<>ToString[NIntegrate[PDF[StudentTDistribution[n],x], {x,r,Infinity}]], {3, .2}]
}
},
AspectRatio->.6,
Axes->True
],
{r,0,4},
{n,1,16,1}
]