How can I display the of result count of a view in its header? Without writing using any Drupal db functions, how can I display the total/count/number of results of a view in its Header?
Do you not mean these predefined value(s) in the Header area ?

Return a view&#39;s total_rows in Drupal 7 without php filter?

You could count the number of rows using PHP in views_pre_render() ... but I bet this is what the above is doing already ....