Activiti provides Query API so there is no need to query act_hi_taskinst
directly.
You query may look like this one
NativeHistoricTaskInstanceQuery taskQuery = historyService.createNativeHistoricTaskInstanceQuery();
taskQuery.sql("SELECT * FROM "+ managementService.getTableName(HistoricTaskInstance.class)+" WHERE start_time_=#{startTime} AND end_time_=#{endTime}");
taskQuery.parameter("startTime", startTime).parameter("endTime", end_time);
List<HistoricTaskInstance> tasks = taskQuery.list();