hummm ... never heard of a shell element with integration points through the thickness ... 4 node or 8 node shells.

as for "optimum" ... there is no optimum ! more integration allow for more complex shape functions which will map complex stress fields with fewer elements.

another day in paradise, or is paradise one day closer ?

In Abaqus, those are called section points but they are basically a form of integration points - stresses are calculated at a few locations in the through-thickness direction to provide more accurate results. So each material point (typical integration point) has a few locations below and above where results are computed. This is especially important for layered (composite) shells.

In most cases default number of section points in the software is sufficient but sometimes you may want to increase their number (if you need more accurate results) or decrease it a bit (if you want to reduce the computational requirements of the analysis).

so these are "just" stress calculation points, combining stresses due to in-plane and out-of-plane loads. Why any different to inner and outer surface stresses ?

another day in paradise, or is paradise one day closer ?

@FEA way
So can we say Its like mesh sensitivity analysis so we increase it until stress results don't change anymore?

Here's a short quote from the Abaqus documentation: Abaqus uses numerical integration to calculate the stresses and strains independently at each section point (integration point) through the thickness of the shell.

By default, there are 5 section points so not only in the middle and at outer surfaces but also between these three locations. And there can be more if needed for some specific nonlinear cases. For linear analyses, 3 should be enough.

The same nomenclature is used for beam elements, by the way.

A mesh sensitivity study is usually performed by just increasing the number of elements, there's rarely a need to increase the number of section points as well.