definite integral please help

(a) y = ln(1+e^x)
dy/dx = 1/(1+e^x) * e^x = e^x/(1+e^x)
∫e^x/(1 + e^x) {0,1} = [ln(1+e^x)] {0,1}
= ln(1+e) - ln 2
= ln[(1+e)/2]

(b) ∫1/(1+e^x) dx {0,1}
= ∫(1+e^x - e^x)/(1+e^x) dx {0,1}
= ∫dx {0,1} - ∫e^x/(1+e^x) dx {0,1}
= [x] {0,1} - ln[(1+e)/2]
= 1 - ln[(1+e)/2]
= ln e - ln[(1+e)/2]
= ln[2e/(1+e)]