Find primitive $F$ of $f(x) = e^x-2x$ that satisfies $F(1) = e -3$

Question

$$f:\mathbb R \to \mathbb R , f(x)=e^x-2x$$

Find primitive $F$ of $f(x)$ that satisfies $F(1) = e-3$.

$$F(x)=e^x-x^2+C$$

I am really confused by the subject of primitives, I very rarely get exercise that refer them. How should I approach this exercise? The way I understand it, a continuous function has infinitely many primitives that differ by a constant? Does this exercise sum up to finding the value of $C$ that satisfy the equation $F(1)=e-3$ then ?

Answer 1

You're almost there: We want $e -3 = F(1) = e^1 - 1^2 + C$. Solve for $C$.