How to compute a matrix from a given basis?

Question

Let V be the $C$-vector space with basis $B$ := $(1,\cos(x),\sin(x))$.

Define the linear operator $$J:V→V \text{ by } (J[f])(x):=\int _0^{\pi }\:f\left(x-t\right)dt$$ for all $f∈V$.

How would one come up with the matrix J with respect to this basis?