I am using ESRI ArcGIS 10.1.
I have a line which has been dissolved, having initially been composed of 4 features. I want to remove these parts, properly dissolving it into one continuous feature. I tried using the Unsplit Lines tool but no luck.

Additionally, once dissolved it places the final vertex at a mid point, not the end of the line:

This proves very difficult to manually correct. Curiously, the position of the end point is the end point of the right most line from the four that this was initially dissolved from.
If anyone knows how to get ridd of these parts, I'd appreciate it.
I am wondering if it is because there is an infinitessimally small distance between parts, but it seems they're snapped together.