Angular momentum, rotating cylinders,...

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Revising, this is what I'm stuck on: inertia tensors, rotating rigid bodies about axis other than its axis of symmety,...

I think it'd help a lot to see a worked example and I can't find anything on the web. Here is my example:

Considering a cylinder of unit density occupying the region x²+y²<=a², 0<=z<=h, what is its angular momentum about the axis x=z,y=0? Can you explain to me how to get there? This is very general so I think I'll be able to generalize it when I understand this one!

Any help would be amazing! Thank you