Function strike_integral 

fn strike_integral<R: Scalar>(
    convention: VolConvention,
    forward: R,
    at: R,
    call: bool,
    spreads: Option<&[f64]>,
    sd_at: &impl Fn(f64) -> Result<R, PricingError>,
) -> Result<R, PricingError>

∫ of the call from at (a spread to the forward, in the mode) up, or of the put from below up to it, over the smile quoted at spreads (flat at the at-the-money vol when there is none): the flat wings in closed form, the smile between its pillars by Gauss–Legendre. The piece the strike bounds is integrated in the mode, so its moving end differentiates.