This paper first proposes an integral function algorithm of the support vector machine model for path optimization of physical education and health courses in colleges and universities according to the core literacy integration teaching situation. Secondly, the integral function algorithm is used to map the initial data from the original space to a higher dimensional space so that the samples exhibit linear differentiability in the higher dimensional space and the significance and correlation of the factors influencing physical education and health in colleges and universities are analyzed using spatiotemporal sequences. Then a physical education and health test management system was constructed according to the needs of physical education teachers and students, while an integral function algorithm was used to analyze the behavior of physical education and health knowledge in colleges and universities. The results showed that there was a significant difference (p>0.05) between the knowledge of physical education and health ( X ± SD ) for 10.6 ± 4.5 and physical education and health behavior ( X ± SD) for 7.2 ± 3.5 showing that there was no significant difference between the knowledge and behavior of physical education and health, which can be considered to have a high degree of consistency in knowledge and behavior.