hiintegrate integral from 0 to t of e^s sin(t-s)ds.
Simply apply the by parts rule, you will get the answer
Here's the first bit:
Is that OK? I've integrated to get , and differentiated to get .
Now use Parts again on the second integral, and you'll find you get back to the integral you started with. Put this equal to , and solve.
See if you can complete it now.