Start by drawing a picture. Include the start ($S$), the finish ($F$), the four points and the forbidden circles of radius $1$ around each of them:
You may not enter any of the red areas. Apart from that, you should follow the shortest possible path, the one a tight rubber band would use. There are essentially two options to consider: the upper path and the lower one. The upper is two units up, then a semicircle, then one unit down:
$$2 + \pi + 1 \approx 6.1416$$
The lower path has a quarter circle, then one unit right, then a semicircle:
$$\tfrac12\pi + 1 + \pi \approx 5.7123$$
so the lower path is the shorter one.