Let x be the angle in degrees, so the angle in radians is:

So you want to integrate:

using standard sin and cos functions in radian.

Since

we get:

And its integral is:

So the result in degrees is (using cosines in degrees):

I don't know the solution given by these packages but the difference between their results and the one I gave above should be a constant. Please notice that there are many ways to represent trigonometric identities so it is possible that two very different looking expressions are equal.