I have widely seen this format for cost
$$ J(\boldsymbol{x},\boldsymbol{u}) = \boldsymbol{x}_f^T\boldsymbol{H}\boldsymbol{x}_f + \int_{t_0}^{t_f}{[\boldsymbol{x}^T\boldsymbol{Q}\boldsymbol{x} + \boldsymbol{u}^T\boldsymbol{R}\boldsymbol{u}]}dt $$
But I also saw this on Wikipedia
$$ J(\boldsymbol{x},\boldsymbol{u}) = \boldsymbol{x}_f^T\boldsymbol{H}\boldsymbol{x}_f + \int_{t_0}^{t_f}{[\boldsymbol{x}^T\boldsymbol{Q}\boldsymbol{x} + \boldsymbol{u}^T\boldsymbol{R}\boldsymbol{u} + 2\boldsymbol{x}^T\boldsymbol{N}\boldsymbol{u}]}dt $$
I really think that this $2\boldsymbol{x}^T\boldsymbol{N}\boldsymbol{u}$ isn't right...
Is it?