You need to use the following substitution `pi*t = u` , such that:
`pi*t = u=> pi*dt= du => dt= (du)/(pi)`
`int sin(pi*t)dt= (1/(pi))*int sin u du`
`(1/(pi))*int sin u du= - cos u + c`
Replacing back `pi*t` for u yields:
`int sin(pi*t)dt = -(1/(pi))*cos(pi*t) + c`
Hence, evaluating the indefinite integral, yields `int sin(pi*t)dt = -(cos(pi*t))/(pi) + c`
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