Okay, so let me see if I understand you correctly. First, it looks like you have two variables
t and
T. Are those different or are they supposed to be the same? Assuming they're different variables, then the given problem looks something like this:
If
∫0Tcos(x)dt=A, find
∫0Tsin(x)dt
Since we're integrating the cosine of
x with respect to
t, we can treat it as a constant. i.e.
∫0Tcos(x)dt=cos(x)⋅[t]0T=T⋅cos(x)=A. Unless, of course,
x is meant to be a function of
t, in which case I believe we'd need to know how the two variables are related in order to proceed.