Integration can be quite a daunting topic if your fundamentals in both algebra and differential calculus aren't solid. If you're falling behind in class and then feeling overwhelmed by the content and work load, you need to spend some time away from class polishing your basics so that everything will become a lot easier - though, this is easier said than done! I would recommend using Khan Academy. I learnt differentiation and integration (as well as a load of other topics) using Khan Academy when I was in year 9 so it's definitely easy to follow along. The teaching obviously doesn't line up exactly with the A level syllabus but maths is maths lol. Just click on the topics you need to learn! (It's great for maths in general and it will definitely have everything on the A level course just not neatly laid out - you'll need to search for specific subtopics on the courses). Here are the links to differential and integral calculus but go ahead and look through the website for any other topics you're shaky on:
Differentiation (You can skip the limits and continuity chapter if you want - it's not relevant to A level):
https://www.khanacademy.org/math/differential-calculusIntegration (You only really need the first chapter labelled 'Integrals' and then some of the next, 'Differential equations':
https://www.khanacademy.org/math/integral-calculusLet me know if you have any more questions; I'm happy to help