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).