Expected P&L and drift

(a) Prove Proposition 9.4(b): with $\mu=r$, the expected discounted P&L of a long option bought at $\sigma_i$ and hedged continuously at $\sigma_i$ is $BS(\sigma_r)-BS(\sigma_i)$. (b) For $S_0=K=25{,}000$, $T=30/365$, $r=6\%$, $\sigma_i=14\%$, $\sigma_r=11\%$, the formula (9.14) gives a seller's expected profit of 84.74 points if $\mu=6\%$ and 82.84 if $\mu=15\%$. Explain the sign of the difference using the dollar-gamma weighting. (c) Does (b) contradict the statement that "a delta-hedged option is not a directional bet"? Be precise.