Fourier transform on L1

[Bridgeport]

Could you help.?

Prove that if $f\in L^1(\mathbb{R})\cap L^\infty(\mathbb{R})$ and $\hat{f}\geqslant 0$, then $\hat{f}\in L^1(\mathbb{R})$ with $||\hat{f}||_1\leqslant ||f||_\infty$

Clarifications:
^ - fourier transform

Orgomnoe spasibo!