Why can't I substitute a Laplace transform into an integration?

hyphagon
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Hi, I was given the attached question and have given my wrong attempt at the answer. I know how to work the answer out (also shown) but I would like to know why my first attempt is wrong.

Many Thanks
 

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First, you calculated u'(t) incorrectly. Second, when you said v=2/s2, you used the definite integral of dv/dt. You need to use the indefinite integral. You can't get rid of the t dependence.
 
Yup, I integrated it by mistake. That now makes it equal zero incidentally.

Awesome, Thanks for for that. Makes sense now.
 

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