How to find 2 constants in a probability distribution function?

Question

How to find a and c in this function? In the example they are using limits, but I don't exactly understand why and how.

The answer is: $a = -1, c = 0$

Answer 1

When $x = 1$, the cumulative distribution must be continuous with value $1$, so $a \cdot 1^2 + 2 \cdot 1 + c = 1$. Also, at $x = 0$ the distribution must be continuous with value $0$, so $a \cdot 0^2 + 2 \cdot 0 + c = 0$. From the second equation, $c = 0$. Plugging into the first gives $a = -1$.

Here's the function: