Here are the correct answers:

1. True – If a function $f$ is an injection (one-to-one function), then no two different elements in the domain are mapped to the same element in the codomain.

2. Not True – A function $f$ may not be continuous at $a$, but it can still have a limit at $a$. Discontinuities such as removable and jump discontinuities still allow limits to exist. Only essential discontinuities might make the limit undefined.

3. Not True – An integral function (antiderivative) is not unique because indefinite integrals include an arbitrary constant $C$, meaning a function has infinitely many integral functions.

Would you like more details or explanations?

Related Questions:

1. What is the difference between injective, surjective, and bijective functions?
2. How can a function be discontinuous but still have a limit?
3. What are the different types of discontinuities?
4. Why does an antiderivative always include a constant $C$?
5. Can a function have a unique integral function under specific conditions?

Tip: When solving limit problems, always check if the left-hand and right-hand limits exist and are equal!