You've used several parameters in your polynomial and the pattern you describe (low integrity in 2nd and 5th semester) is very odd and contrary to reasonable expectation. In this situation, I think you'd be much better off treating semester as a categorical variable and not continuous.

Other concerns:

1. Your model explains just ~3% of the variance ($R^2$), which is very low.
2. You are treating your integrity measure as continuous instead of ordinal. This may be reasonable but is worth thinking about.

You've used several parameters in your polynomial and the pattern you describe (low integrity in 2nd and 5th semester) is very odd and contrary to reasonable expectation. In this situation, I think you'd be much better off treating semester as a categorical variable and not continuous.

Other concerns:

1. Your model explains just ~3% of the variance ($R^2$), which is very low.
2. You are treating your integrity measure as continuous instead of ordinal. This may be reasonable but is worth thinking about.

EDIT based on the information that 2nd and 5th semesters are meaningfully different:

I would still be inclined to treat semester as categorical if you want to make a simple model that only includes semester. But if you are willing to consider building more complex models, you could could account for practical/university semesters with a factor and use a simpler continuous time trend for semester (I would starting by considering just a linear relationship).