I can see that the values of the PersonnelIds is written as string "[31,32,33,34]"
so to parse it with this syntax you can use the following code
JObject jObject = JObject.Parse(myjson);
JToken jToken = jObject.GetValue("PersonnelIds");
var array = JArray.Parse(jToken.Value<string>()).Select(x => (int)x).ToArray();
if your value is not string so your JSON is like {"PersonnelIds": [31,32,33,34]
}
then you can parse it using the following code
JObject jObject = JObject.Parse(myjson);
JToken jToken = jObject.GetValue("PersonnelIds");
int[] array = jToken.Values<int>().ToArray();