Can I trust my cycle?

I know a woman has a chance of getting pregnant any day of the month no matter how small. I've been doing research and I read that the day right before your expected period and the first day after your period are the least fertile days if you have a perfect regular cycle. I want to know if this is accurate information? My cycle is extremely regular and I was thinking if this information was true. Would I be okay to have sex without a condom and only my birth control? (also to clarify he would cum in me which is why I'm being so particular?