WHat is not shown is a gain control pot for the 1k resistor in the bottom right corner to ground.
The 1st stage has ● HIGH OPEN-LOOP GAIN: 160dB
● LOW INPUT BIAS CURRENT: 10nA max
● LOW OFFSET VOLTAGE: 75µV max
The cap added tends to improve the phase margin and cuts lower than the internal cap put in all internally compensated OA's
The 2nd stage is a power amp with x10 R ratio gain
So you can see the out has 2 series 1K resistors , where the middle can be tapped to ground to attenuate the feedback which boosts the gain from unity gain up to high values. So the POwer Amp has local gain but in this design with 2 stage negative feedback the overall gain is determined by comparing the input with speaker output feedback to the 1st stage and seeing what the negative feedback resistor ratio is. So if a 100 Ohm to ground was added off the sheet, you have 10:1 reduction in feedback and thus 10:1 controlled gain with 180dB open loop gain available.
Since there is loss of phase margin with 2 stages cascaded, these power Amps also tend to oscillate at low gain high bandwidth at the unity gain resonant frequency , so the 1 Ohm load and series cap loads the spurious oscillation tendency with 1 Ohm > 50KHz to prevent it frying up with full scale RF.
Classic Audio power amp trick. So the 1st cap is not just an integrator to remove DC offset as the DC offset is removed by DC feedback loop. (1K"s in bottom right corner, so the typed info is misleading , if one did a BODE plot for phase margin , you might see the effects better.
The rest are two type of caps to minimize ESR over the frequency range on each supply rail to minimum noise, hum and shot noise. Ferrite beads might help too.