Q1: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function and $F: \mathbb{R} \rightarrow \mathbb{R}$ be an antiderivative of $f$. Is $G = F+2$ also an antiderivative?

A1: Yes!

A2: No, never!

A3: No, not necessarily.

Q2: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function and $F,G: \mathbb{R} \rightarrow \mathbb{R}$ be two antiderivatives of $f$. What is $F-G$?

A1: $\sin(x)$

A2: a constant

A3: $x$

A4: In general, it could be anything.

Q3: What is the integral $\int_0^x \cos(t) , dt$?

A1: $0$

A2: $\cos(x)$

A3: $\cos(\exp(x))$

A4: $\sin(x) $

A5: $\cos(\sin(x))$