They do anti-derivatives in Calculus 1, in universities. They usually don't learn about Riemann sums and such until the next course in Calculus. These question were probably assigned or done in lecture and he doesn't understand them.
If your given a function we're basically trying to find a function such that
Knowing this we can reverse some of the easier differential rules.
Like the power rule. if then
Since the derivative of a constant is 0.
Or with cos and sin. if then
For the first question note that:
For the second question, a helpful identity is that