integration - Evaluate $lim_{nto infty} sum_{i=1}^nleft(cos^2left(frac{pi i}{n}right)right)frac{pi i}{n}$

Evaluate $$\displaystyle\lim_{n \to \infty} \sum\limits_{i=1}^n\left(\cos^2\left(\frac{\pi i}{n}\right)\right)\frac{\pi i}{n}$$

My answer is $$\int\limits_0^1{\pi x\cos^2(\pi x)dx}$$
but I do not know how to solve this. If integrating by parts, should I differentiate $\cos^2(\pi x)$ or $\pi x$? Because differentiating the former leaves one with a long integral with $x^2$ and two trig identities, and differentiating the latter is complicated because of the x that needs to go with it in $uv - \int v du$. I did not get much success either with substituting $u=\pi x$