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Locating center of object

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I'm sure this is a simple task, but I'm just not quite sure where to look. I have a vertex buffer full of my complete mesh, but I have a separate index buffer for each individual piece of the mesh. The problem I've ran into is I'd like to have precalculated center points per each individual piece of the mesh, but I'm either unaware of the DirectX call to attain it or if I need to do the math myself then I am definitely clueless. I'll need to calculate a bounding box per piece anyhow, so should I be looking to do that first and then locate the center of the bounding box?

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