I came across a strange problem

The first question asks me to find the fourier transform of $g(t)$, but it is given graphically so I need first to find the correct analytic expression, which is some sort of combination of $rect, triang, sinc, Sa$ and all the functions used in Signal's theory. In the interval $[-T, 0]$, the teacher suggests to consider the inclined part of the signal as the integral of a determined function (I later found out it must be the integral of a rect). The teacher also added that I should (???) remove the step function in order to get it correctly.
Can you please explain to me how I should find the Fourier transform, comprehensively? Thanks.