p. 605, 92.

The function \(TraditionalForm
      \`erf(x)\  = \ 
        ∫\_0\%x\(\( 2  e\^\(-t\^2\)\)\/\@π\) 
            dt\) is built into Mathematica.

?Erf

You can find more information about this function in the Help Browser.

Plot[((2  (E^(-(t^2))))/(Sqrt[π])), {t, 0, 3},  
      PlotRange -> {0, 1.25}]

Plot[Erf[x],  {x, 0, 25},  PlotRange -> {0, 1}]

Since (e^(-(t^2))) ≤  (e^(-t)) for t  ≥  0, and the integral \(TraditionalForm
      \`\(2\/\@π\) 
        \(∫\_0\%∞\( e\^\(-t\)\) dt\)\) converges (to (2/(Sqrt[π]))), the integral \(TraditionalForm
      \`\(2\/\@π\) 
        \(∫\_0\%∞\( e\^\(-t\^2\)\) 
            dt\)\) must converge also. Its value i the limit of erf(x) as x -> ∞. The above plot indicates that this limit is 1.

Limit[Erf[x],  x -> ∞]