$$f(x) = 1_{[-1,1]} (x)$$
I’m not familiar with the f(x) notation. It’s 1x with a subscript of the interval next to the 1 followed by x. Does this mean it’s equal to 1x on [-1,1] and undefined elsewhere. Also it’s asking me to take the Fourier transform of f, which I thought was only on the interval infinity to negative infinity.
This is the indicator function.
$$f(x)=1_{[-1,1]}(x)=\begin{cases}1&x\in[-1,1]\\0&x\not\in[-1,1]\end{cases}$$
To compute its Fourier transform is simple, you integrate this function over $(-\infty,\infty)$ as usual, but since the function is zero outside this specific range, the integral limits become $\int_{-1}^1$.