Application of calculus in real life I'm no mathematician, so bear with simplicity of what I'm asking.
My calculus course(post-Soviet country, a while ago) was utter trash. I've recently decided to approach the topic for self eduction.
I'd like to know how all of it is being applied IRL. 
The textbook examples on differentiation and integration use convenient incomes to be typical and easy to solve. But how would I start with computing intergal of a real-life function, with 'non-textbook' equivalents?
How do I compute derivative from speed change graph of real-life wehicle which stops, speeds up in 'undeterministic' manner?
 A: Honestly, I do not think there are any non-trivial "real life" applications that would be solved with undergrad level calculus. By "un-deterministic", I assume you mean stochastic and calculating "derivatives" of stochastic processes requires substantially heavier mathematical machinery than standard calculus. Now, if you are referring to the contrived "real world" word problems often found in calculus books, that is a different story. If you really want to use mathematics to solve "interesting" problems (I guess this is more of a matter of taste), I recommend furthering your body of knowledge. 
Most "real world" problems are solved via numerical analysis so you might want to consider taking a look at that but even numerical analysis relies on many important concepts from analysis that will not be taught in calculus. Now, as counter-intuitive as it sounds, I'd recommend getting a solid foundation in the theory (especially in the big 3 of  linear algebra, real analysis and functional analysis) before you worry about the applications. It will be difficult to solve an original problem without a through understanding of these topics.
I recommend most people start with Sheldon Axler's Linear Algebra Done Right and supplement it with a more computational text like Strang. After that, maybe start with Understanding Analysis by Abbot (again supplement this with a more computational text) then proceed to Baby Rudin or Erwin Kreyszig's Introductory Functional Analysis with Applications. Once you can understand these, you will be much better positioned to formulate and then solve your own problems.
