Yes it is correct. Also, as Manohar mentioned, double integration of the first derivative of ESR a very standard method (I have about 25 publications on the ESR, EPR area )
I agree fully with the answer of Michael for the " high school mathematical question/Power 23 a.s.o." and his remark about the number of spin concentration (would refrain..).
The another answers are correct too.
However your question :
How can I calculate spin concentration from known concentration of any sample to put input in EPR instrument ?
is formulated very, very bad! Why?
You introduce the Avogadro' s Number or Avogadro constant and link it with the mmol Tempol quantity.
As you know, the Avogadro constant links the atomic and macroscopic properties of matter.
But how do you put this input in the EPR spectrometer? What a kind of spectrometer are you using? Bruker or AEG ??
What a solvent are you using for your Tempol solution? Do you want to link Tempol with a molecule and to study the delocalization of the radical over the new molecule?
The second integral can offer reliable value only when the base line is correct. The computer simulation can give reliable value, even in this case. For kinetic studies I found the "noise" of determined concentration curve is much smaller, when correct signal fit is obtained.