Question: How do I get this answer?

It is very stranger that these two statements are not equative:

evalf(Int(x*sin(x)/(1+(cos(x))^4),x=-Pi/2..Pi/2));

 1.845096351

 evalf(int(x*sin(x)/(1+(cos(x))^4),x=-Pi/2..Pi/2));

 1.323830675+0.*I

I think the first one is correct. In fact, the exact result is

 2*hypergeom([1/4, 1/2, 1, 1], [3/4, 5/4, 5/4], -1);

u can evalf the above answer to check it. In fact, Maple cannot get this analytic answer, how do I get it?

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