Integration trig help??

Question

Find ∫[high π/2, low 0] cosx e^sinx dx

Answer 1

Let sin(x) = u so cos(x)dx = du

The limits become:
x=pi/2 and u = sin(pi/2) = 1
x = 0 and u = sin(0) = 0

Equation is then: e^u du which when integrated gives e^u
So evaluate this from 0 to 1
Answer = e - 1