Calculate integrals using Euler-Maclaurin's formula. I am trying to calculate the following integral using Euler-Maclaurin formula. Found the end resault using an online intergrals calculator but I can't seem to get there on my own. 
$$  \int_0^1 e^{-x^2} $$
I need an explanation on how to use the formula to calculate the integral and an explanation on what exactly is p in the formula.
Here is the Euler-Maclaurin's formula from wikipedia:
$$ \sum_{i=m}^n f(i) = 
    \sum_{k=0}^{2p}\frac{1}{k!}\left(B^\ast_k f^{(k - 1)}(n) - B_k f^{(k - 1)}(m)\right) + 
    R $$
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\begin{align}
&\int_{0}^{1}\expo{-x^{2}}\,\dd x
=\half\int_{0}^{2}\expo{-x^{2}/4}\,\dd x
\\[3mm]&\approx\half\braces{\sum_{k = 1}^{1}\expo{-k^{2}/4} + \half\bracks{1 + \expo{-2^{2}/4}}
- {1 \over 12}\bracks{-\,\half\,2\expo{-2^{2}/4}}}
\\[3mm]&=\half\,\expo{-1/4} + {1 \over 4} + {7 \over 24}\,\expo{-1}
=\color{#c00000}{0.746}6985619
\\[5mm]&\mbox{A more precise numerical integration yields}\quad 0.7468241328
\end{align}

The exact result is $\ds{\half\,\root{\pi}{\rm Erf}\pars{1}}$.

Information of the remainder can be seen in $\quad\large\tt\mbox{page 886}\quad$ of
  this table.

