On the integral $ I_s = int_ {1} ^ { infty} ( pi (x) -Li (x)) x ^ {- s-1} dx $

To define $ pi (x) $ be the first count function and Li (x) the logarithmic integral. Let $ I_s $ to be defined as above.

is $ I_s $ known to be convergent for any real number $ s <$ 1 ?