Goursat's theorem with a bounded isolated singularity

Let \(f ( z )\) be analytic in an open set Ω except possibly at a point \(z _ { \mathrm { 0 } }\) inside Ω. Show that if \(f ( z )\) is bounded in near \(z _ { \mathrm { 0 } }\) , then \(\int _ { \Delta } f ( z ) d z = 0\) for all triangles \(\Delta\) in Ω.