Is my prayer valid after forgetting the last Tashahhud, returning to it, then performing the prostration of forgetfulness (sujud al-sahw) before the Taslim?

If the nafila (supererogatory prayer) is a ratiba (regular sunnah prayer), then what the worshipper did is correct. However, if it is an absolute nafila (unrestricted supererogatory prayer), then he must sit down and then choose one of two options: either he recites the tashahhud and performs the two prostrations of forgetfulness (sujood al-sahw) and then says the tasleem, or he intends an increase in the number of rak'ahs and then stands up to complete what he intended. It is permissible to intend an increase or decrease in an absolute nafl prayer on the condition of changing the intention beforehand; otherwise, the prayer becomes invalid if the increase or decrease was deliberate and without changing the intention. However, if he was forgetful, the prayer does not become invalid; rather, he returns to the sitting position, recites the tashahhud, and performs the prostrations of forgetfulness. If he intended an increase while standing, the well-known opinion is that he must return to the sitting position before standing for the increase, and he performs the prostrations of forgetfulness at the end of his prayer. If he prayed four rak'ahs out of forgetfulness after intending two, and then intended to complete it as four, he prays two more rak'ahs, and what he did out of forgetfulness is not counted. If he intended four rak'ahs and then intended to limit it to two, he may do so and say the tasleem after them. If he said the tasleem before changing the intention deliberately, his prayer is invalid. If he said the tasleem out of forgetfulness, he completes four rak'ahs and performs the prostrations of forgetfulness.