  We obtain the asymptotic formula with an error term $O(X^{\frac{1}{2} +
\varepsilon})$ for the smoothed first moment of quadratic twists of modular
$L$-functions. We also give a similar result for the smoothed first moment of
the first derivative of quadratic twists of modular $L$-functions. The argument
is largely based on Young's recursive method [19,20].
