  We present a simple yet powerful and applicable quadrature based scheme for
constructing optimal iterative methods. According to the, still unproved,
Kung-Traub conjecture an optimal iterative method based on $n+1$ evaluations
could achieve a maximum convergence order of $2^n$. Through quadrature, we
develop optimal iterative methods of orders four and eight. The scheme can be
further applied to develop iterative methods of even higher order.
Computational results demonstrate that the developed methods are efficient as
compared with many well known methods.
