(A) lay in the fact that he integrated these
Even though A is grammatically correct. It sounds wordy when compared to option D which is much more concise. Eliminate
(B) lay in the fact of his integrating these
Again this option is too wordy and repetitive. Eliminate
(C) laid in the fact of his integrating these
Past tense Laid is used here which is incorrect to state a general fact. Eliminate
(D) lay in his integration of these
This option is clear, concise and grammatically correct. Hence
correct choice(E) laid in his integration of these
same error as in C. Eliminate