Is this integral wrong?

Question

I use Visual calculus (a website, google it) to practice my calculus. However, I stumbled upon this problem, and I think the website is wrong, I need a second opinion! The integral is as follows: 2e^x - 5 cos (x) dx, from [0, pi]. The websites answer is: 2e^pi - 2, however, I get 2e^pi - 7... This is the website, problem #5, thanks! http://archives.math.utk.edu/visual.calculus/4/ftc.10/index.html

Answer 1

When you integrate 2e^x - 5*cosx, you get
2e^x - 5*sinx
Applying the limits 0 to π, you get
2e^π - 2e^0 - 5*(sinπ - sin0)
= 2e^π - 2
The site is correct.

Remember sinπ = 0 NOT 1

Answer 2

Their answer is correct

sin(pi) and sin(0) = 0 so that part of the equation falls out

so you are left with 2e^pi -2

Answer 3

Their answer is correct. 5(sin(pi)- sin (0)) = 5*0 = 0

Answer 4

int (0, pi) 2e^x - 5 cos (x) dx
= [ 2e^x - 5sin(x) ] (0,pi)
= ( 2e^(pi) - 0 ) - ( 2e^0 - 0 )
= 2e^(pi) - 2.