Integration Output Doesn't make sense
Another thing that might be worth mentioning is that it's not an actual integrator that you got there. It may mimic one and fool you. 

Here's a schematic of how an actual integrator would look like. Also, look at the size of the "R8" I'm using. It's 100 kΩ here, not 1 kΩ. 1 kΩ is way too small. 



As you can see, I'm simply integrating a square wave, the actual integrator shows a triangle wave, as it should. While the bottom "integrator" which you are using show a triangle wave on top of the square wave input. 

Here's the link in case you want to simulate it and see for yourself. 



To make this answer appear less as a comment. The reason for why your output voltage is drooping is because of R8. Your small capacitor (only 1 nF) is discharging through a very small resistor (R8). 

And to answer the title "Integration Output Doesn't make sense", well that's because it's not proper integration as I proved above with the circuit simulation.