Clear[f]
f[t_] := 
      2 + t /; -2 ≤ t ≤ 
          0
f[t_] := 2 - t /; 0 < t ≤ 2
f[t_] := 0
Plot[f[t], {t, -4, 4}, 
      PlotStyle -> {RGBColor[0.4, 0.6, 0], Thickness[0.008]}, 
      AspectRatio -> Automatic, 
      AxesLabel -> {"t", "c(t)"},  
      ImageSize ->  {400, 150}, 
      PlotRange -> {{-4, 4}, {-0.5, 
            2.5}}]
(∫_(-2)^0)(2 + 
            t)*(E^(-I*ω*
              t)) \[DifferentialD]t
(∫_0^2)(2 - 
            t)*(E^(-I*ω*
              t)) \[DifferentialD]t