Understanding a dual op amp integrator circuit
The amplifier U11 drastically increases the open-loop gain of the circuit. As a result, the low-frequency error of each opamp based inegrator (due to the limited open-loop gain Aol of an opamp) is shifted to smaller frequencies.

That means: The lower cut-off frequency fc (where the desired 20 dB drop starts) is much lower. Example:  


One opamp with Aol=1E4 and R=1k, C=1µF, fc=10 mHz
Two opamps with Aol=1E4 and R=1k, C=1 µF, fc=1E-6 Hz 


Comment 1: The resistive divider at the output of U11 has nearly no influence on the cut-off. The divider has the task to reduce/adjust the gain of the first opamp to ensure stability against oscillations.

Comment 2: Without the external elements R and C the shown opamp combination is one of the classical dual-opamp circuits for gain enhancement (composite amplifier). Such a combination is used not only for gain increase. Sometimes such a structure is used to combine the good offset properties of a voltage-controlled opamp with the excellent slewing properties of a current-feedback amplifier (CFA).

Ref: Sergio Franco, "Design with opamps and...", chapt. 8.6.