In a paper of Heier and Wong, It is written that from a pointwise argument due to Berger does follow that the scalar curvature (and thus also the total scalar curvature) of a Kaehler metric of positive holomorphic sectional curvature is also positive. I am looking for the paper of Berger ("Sur les varietέs d'Einstein compactes, C.R. IIIe Reunion Math. Expression latine, Namur (1965) 3555") to which Heier is referring, but I don't have access to Berger's paper so I ask here to see if this can be proved very quickly or has been written in somewhere else.
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The answer to your question is exactly the same of the answer to this older question of mine. Enjoy! 

