Cybersecurity education is considered an important part of undergraduate computing curricula, but many institutions teach it only in dedicated courses or tracks. This optionality risks students graduating with limited exposure to secure coding practices that are expected in industry. An alternative approach is to integrate cybersecurity concepts across non-security courses, so as to expose students to the interplay between security and other sub-areas of computing. In this paper, we report on our experience of applying the security integration approach to an undergraduate web programming course. In particular, we added a practical introduction to secure coding, which highlighted the OWASP Top 10 vulnerabilities by example, and demonstrated how to identify them using out-of-the-box security scanner tools (e.g. ZAP). Furthermore, we incentivised students to utilise these tools in their own course projects by offering bonus marks. To assess the impact of this intervention, we scanned students' project code over the last three years, finding a reduction in the number of vulnerabilities. Finally, in focus groups and a survey, students shared that our intervention helped to raise awareness, but they also highlighted the importance of grading incentives and the need to teach security content earlier.