Moreover regarding my last question,

If I am to integrate (1- cos^5(theta))d(theta) from 0 to pi/2, can I split the integral into:

1d(theta) from 0 to pi/2 minus cos^5(theta)d(theta) from 0 to pi/2?

I then make the substitution u = sin(theta), thus, du = cos(theta)d(theta). Moreover, 1 - u^2 = 1 - sin^2(theta) = cos^2(theta). Therefore the integral for cos^5(theta)d(theta) from 0 to pi/2 is equivalent to integral of

(cos^2(theta))(cos^2(theta))cos(theta)d(theta) from 0 to pi/2 which is equivalent to integral of (1 - u^2)(1 - u^2)du from 0 to 1 (these new limits found by u = sin(theta) from 0 to pi/2).

By the described method above (splitting the integral) I get an answer of:

of (pi/2 - 8/15)

However when doing the same integral for 1- cos^5(theta))d(theta) from 0 to pi/2 using the table of integrals I get an anwer different from the above?!

Thanks again