Consider 2 continuous mapping from $[0,1]$ to a topological space $X$
$$F:[0,1] \to X$$ $$G:[0,1] \to X$$
We have $F([0,1])=G([0,1])$. My question is whether $F$ and $G$ are homotopic. If it's not true in the general case then what property $X$ needs to have for $F$ and $G$ to be homotopic. My intuition is telling me that they should be homotopic since they're the same curve just with different parametrization but I don't have any idea how to prove it