Evaluate: $\int\left(x^{2}-x\right) \cos x d x$

Step 1 ：Given the integral problem \(\int\left(x^{2}-x\right) \cos x d x\), we can solve this using the method of integration by parts. The formula for integration by parts is \(\int u dv = uv - \int v du\).

Step 2 ：We choose \(u = x^2 - x\) and \(dv = \cos(x) dx\).

Step 3 ：We then find \(du\) and \(v\). \(du\) is the derivative of \(u\) and \(v\) is the integral of \(dv\). So, \(du = 2x - 1\) and \(v = \sin(x)\).

Step 4 ：We calculate \(uv = (x^2 - x)\sin(x)\) and \(\int v du = \int (2x\cos(x) - \cos(x)) dx = -2x\cos(x) + 2\sin(x) + \cos(x)\).

Step 5 ：Substituting these into the integration by parts formula, we get \(\int\left(x^{2}-x\right) \cos x d x = (x^2 - x)\sin(x) - (-2x\cos(x) + 2\sin(x) + \cos(x))\).

Step 6 ：Simplifying this, we get the final answer: \(\boxed{2x\cos(x) + (x^{2} - x)\sin(x) - 2\sin(x) - \cos(x)} + C\), where \(C\) is the constant of integration.