What is the ruling on bending close to the ground when rising from prostration to the sitting position between the two prostrations, instead of sitting with a straight back?

Sitting between the two prostrations is a pillar (rukn) of prayer, because the Prophet (peace and blessings of Allah be upon him) commanded it in the hadith of the one who prayed badly, as is tranquility in it. The minimum level of tranquility is stillness, even for a brief moment. So, if the worshipper does not sit upright in his posture, and remains closer to prostration, his prayer is invalidated.