Hölder's inequality: What does $\|\cdot\|_1$ refer to when it's an integral?

Question

Hölder's inequality: What does $\|\cdot\|_1$ refer to when it's an integral?

In the L.H.S. of Hölder's inequality.

Answer 1

$$||f||_1 = \int_a^b |f(t)|dt$$

Answer 2

Let $f \in L^{1}[0,1]$. Then, $||f||_{1} = \int_{0}^{1} |f(t)| dt$.