Let $\displaystyle f(x) = \log{(1-x^2}) $

Let $\displaystyle I_n = \int_{n-\frac{1}{2}}^{n+\frac{1}{2}} \log{x} \ dx - \log{n} $ for n natural.

Show that $\displaystyle I_n = \int_0^{\frac{1}{2}} f\left(\frac{t}{n}\right) dt $

I just can't get this. Any help would be appreciated. Thanks