For integration you need some math textbook. Essential Mathematics for Economic Analysis is good textbook. It has a lot of detailed explanations how to solve various integrals.
For the statistics topics you could have a look at Statistics for Business and Economics by Newbold.
If you want some online resources Khan Academy has videos on all the topics you mention, and they show steps and even have practice exams.
For some personal help you will likely have to find some tutor. You can try some online forums or Q&A site like this one, but sites like this one will ask you to show your own attempt at solution which can be difficult if you don't have any idea how to start solving the problem.
How much time you need to learn this topics depends on various factors.
For example, do you already have good algebra and calculus background, aside from not knowing integration? If not you cannot learn integrals without learning algebra and calculus topics first. If you have good background in math you can pick up integrals in 2-4 days. If you do not know what algebra or calculus is it will take you at least 2-3 weeks of intensive daily study to go from knowing nothing to be able to deal with more difficult integrals.
When it comes to statistics topics you describe it depends again on what level you need to understand these topics on. Bachelor level? The list of topics you provide basically covers what is taught in 101 statistic courses at universities that usually run 2-3 months. If you don't need to study anything else and just focus on this you can probably go through everything in 3-4 weeks. If you need to understand these topics on graduate level you will need much more time.