How to draw a curve line on Pixelmator
The best you can do in Pixelmator 1 is arcs using the oval selection tool. Select an area with the selection tool set to the circle/oval setting and then trace the selection (Edit -> Stroke) on a new layer. Once traced, erase the part of the trace you don't need. Reposition, stretch and mangle with the layer tools.

Pixelmator 2 adds vector drawing capabilities. It'll be available this summer and it will be a free upgrade for anyone who purchased Pixelmator 1 via the App Store.

Update: Pixelmator 2 was released via the App Store today and the pen tool lets you draw and manipulate curves now. Works great.