Volterra integration operator on $C[0,1]$

Let $C[0,1]$ be the $\mathbb R$-vector space of real valued continuous functions equipped with the norm $\|f\|=\sup_{x\in[0,1]}|f(x)|$. Let $T:C[0,1]\to C[0,1]$ be defined as

$$T(f)(x)=\int_0^xf(t)\,dt,\quad\text{for }x\in[0,1].$$

Let $T^n=T\circ T\circ\cdots\circ T$ ($n$ times). Which of the following statements are true?