I am reading at Evans' book *Measure Theory and Fine Properties of Functions, Revised Edition, p. 165* and I can't see how one gets the transition from the first dotted integral to the second one --


We have
[![Hausdorff surface measure][1]][1]


  [1]: https://i.sstatic.net/6joyM.png

-- here $Df$ is just the gradient of $f$ and $d H^{n - 1}$ is the Hausdorff surface measure.

Any help would be much appreciated!