The nLab says the following about closed monoidal functor categories:

Let $C$ be a complete closed monoidal category and $I$ any small category. Then the functor category $[I, C]$ is closed monoidal with the pointwise tensor product, $(F \otimes G)(x) = F(x) \otimes G(x)$.

Now I wonder what the right adjoint of $F \otimes {-}$ is. I suppose, that it fulfills the following equation (which is a generalization of the equation for exponentials in functor categories):

$$(F \multimap G)(x) = \int_{y : I} \prod_{I(x, y)} F(y) \multimap G(y)$$

Is this correct? And if yes, is there a more standard way of representing the right adjoint?