Integration headache, please help.

Integration headache, I simply cannot see how come that this online calculator (see link) gives the result it gives (see link or attached picture). Please help, it is driving me crazy.

 

https://www.wolframalpha.com/input/?i2d=true&i=Integrate%5B-Sin%5Bt%5D*Exp%5B-i*t%5D%2C%7Bt%2C-pi%2C0%7D%5D

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  • Leave a comment if you need any clarifications.

  • The given sin(2t) identity I belive to be wrong, and it can be confusing. But I appreaciate the very fast response. Thank you.

  • Oh, it' a typo. Sin 2t =2 sin t cos t. There is no mistake in the solution, I just dropped the 2 in the last line when I wrote the trig identity.

The answer is accepted.