let $f(x)=\ln\left(1+\frac{x}{2}\right)$ and let $P_6(x)$ be the 6th order interpolating polynomial. We are given points $x_0,...,x_6$, and need to estimate the error $\displaystyle\left|\int_\limits{x_1}^{x_6}f(x)\ \mathrm dx - \int_\limits{x_1}^{x_6}P_6(x)\ \mathrm dx\right|$
Normally when estimating the error in interpolation I'd use the formula $$\frac{\max\big|f^{(n+1)}(x)\big|}{(n+1)!}\big|(x-x_1)\cdots(x-x_n)\big|$$
But I'm not sure what to do here when we are approximating the integral. Do I just find the integral of $f$ and find plug it in the formula, so in this case, basically finding the 7th order derivative of the integral?