I found the following problem on Fourier Series. But I cannot make sense about how $f(x)$ could be a $1$-periodic function on the interval $[-1,1]$? Could you please help me make sense out of this problem?
Let $f$ be the $1$-periodic function such that $f(x) = |x|$ for $x \in [−1,1]$. Determine explicitly a sequence of trigonometric polynomials $(p_N )_N$ such that $p_N \rightarrow f$ uniformly as $N \rightarrow \infty$.