Help with Calculus pls

[xxaxiss]

Hi, I'm currently studying for Calculus BC and want to know how the Riemann Sum and integration connect to each other. I understand the concept of the Riemann Sum, but I'm not sure how the integral works with anti-derivatives. Another problem I have is modeling real life word problems with derivatives and integrals; I'm not sure in which situations to use either. All help is appreciated!