Problem identifying the analytic expression of such determined signal I came across this problem


  


I am supposed to find the Fourier transform of $g(t)$, but I am not able to find the analytical expression of such signal. 

The teacher suggests that I should consider the inclined part in $\left[-T, 0\right]$ as the integral of a determined function. 

It turns out it is the integral of some $\rm{rect}()$ function. However, the teacher noted that I should subtract from it the (???) step function.

Can you explain to me how to find the fourier transform of $g(t)$ more comprehensively?

EDIT 1:

I tried to solve it, and I came to this solution. Is it correct?
The simple answer is “Linearity”

The Fourier Transform is linear.  $g(t)$ can be expressed as a sum of signals that have known, as in there are tables of transform pairs, in most books, probably also in your course notes, along with the shift and scale properties. Look at the tables you have and find entries that you can add to get $g(t))$.  You already found rect().  Look for a triangle piece.  

A full triangle is the convolution of 2 rects.  A half triangle is a full triangle multiplied by a step.