Check my work: Fundamental Theorem of Calculus

[bbl]

I'm not sure of my final answer to applying FTC so any help is appreciated. Thank you!

 

[Steven G]

To be honest, this is too painful to follow. Why did you choose to switch the limits at the beginning? Sure, you are allowed to but it just complicates things. Then you chose to ignore the minus in front and then it appeared again.

 

[bbl]

To be honest, this is too painful to follow. Why did you choose to switch the limits at the beginning? Sure, you are allowed to but it just complicates things. Then you chose to ignore the minus in front and then it appeared again.

I apologize. I realized my mistake. Here is the updated version. I'm still not certain about my final answer so feedback is appreciated. Thank you

 

[BigBeachBanana]

Again, why do you need to split it into 2 integrals? You can but it complicates things.
[math]\frac{d}{dt}\left(\int_{t}^{\sin t}\sqrt{1+u^4}\,du\right)dt=\sqrt{1+\sin^4(t)}\cos(t)-\sqrt{1+t^4}[/math]

 

[Steven G]

You wrote from the FTC you get .....
The .... is NOT the FTC. It is a result of the FTC.
I suspect that you were told to use the FTC and you think that you have to use .....
That is not true at all. Please look up the FTC