The Relationship between Areas Calculated by Riemann Sums and Definite Integrals
Formulas
$$ \begin{align*} & \lim _{ n\to \infty }{ \sum _{ k=1 }^{ n }{ f\left( a+\frac { p }{ n }k \right) \frac { p }{ n } } } \\ =& \int _{ a }^{ a+p }{ f(x)dx } \\ =& \int _{ 0 }^{ p }{ f(a+x)dx } \\ =& \int _{ 0 }^{ 1 }{ pf(a+px)dx } \end{align*} $$
Explanation
Sometimes, you’ll encounter integration problems that are disguised as limit problems. Of course, most of the time you can solve them just by calculating the limit, so not knowing isn’t a big deal.
However, very occasionally, they might ask if you know about that relationship itself. It’s hard to get proficient since it’s not frequently used, but if you have an important exam coming up, it might be a good idea to go over it again.