Losing confidence in Maths in year 13 doing further maths

Are you being taught maths and further maths in parallel?
This might be a case of you not having done enough of regular maths to be able to access the further maths content fully.

Regardless, I wouldn't give up. What about trig integration do you struggle with exactly?

Yeah, we are taught both at the same time. I prefer very methodical maths teaching, but my maths teacher is complete opposite he only writes the final answer on the board and doesn't explain bc we are supposed to be smart as doing further maths : (

I was taught both simultaneously as well, my FM teacher spent a week around the start of year 13 on just regular A-level integration/differentiation so we wouldn't have any problems using it for the rest of the course.
I'd heavily recommend taking some time each day and self teaching it from your normal maths textbooks. The core pure part of FM uses a significant amount of regular maths calculus so you want to be as comfortable as possible.