Multidimensional Gaussian Integral?

Question

I am trying to integrate something of the form $$ I = \int_{-\infty}^{\infty} dx \exp\{-\frac{1}{2}\ \left(\mathbf{d}-x\mathbf{s}\right)^TC^{-1}\left(\mathbf{d}-x\mathbf{s}\right)\}\exp\{\frac{-1}{2\sigma^2}\left(x-\mu\right)^2\} $$ which is of course the same as $$ = \int_{-\infty}^{\infty} dx \exp\{-\frac{1}{2}\ \left(\mathbf{d}-x\mathbf{s}\right)^TC^{-1}\left(\mathbf{d}-x\mathbf{s}\right) - \frac{1}{2\sigma^2}\left(x-\mu\right)^2\}. $$ (note bolded variable are vectors and $C$ is a symmetric square matrix.) So basically I'm convolving two Gaussians, but the variable being integrated is multiplied by a constant ($\mathbf{S}$) in the first term. I've tried working this out to no avail, any thoughts? Thanks.