Prove that $A$ is a compact linear operator.

Question

Prove that for a given two-variable polynomial function $a, $ the operator $A : L^{\infty} \left ([0,1], m \right ) \longrightarrow L^{\infty} \left ([0,1], m \right )$ (where $m$ denotes the Lebesgue measure) defined by $$Af(x) = \displaystyle \int_{0}^{1} a(x,y) f(y)\ dy$$ is compact.

How do I proceed? Any help in this regard will be highly appreciated.

Thanks in advance.