I have an integral `inte1` as below:

    f[x_] := PDF[NormalDistribution[0, 1], x];
    F[x_] := CDF[NormalDistribution[0, 1], x];
    inte1 = Integrate[f[x]*x^2, {x, -∞, k}] // FullSimplify

which is:

[![enter image description here][1]][1]

But I want to show it in terms of `F[x]`:

[![enter image description here][2]][2]

How can I achieve this? Many thanks!

  [1]: https://i.sstatic.net/bUwlom.png
  [2]: https://i.sstatic.net/zRWrTm.png