The varying nature of qualities and costs of the crowdworkers makes task allocation a non-trivial problem in almost all crowdsourcing applications. If crowdworkers are strategic about their costs, the problem becomes even more challenging. Interestingly, in several crowdsourcing applications, for example, traffic monitoring, air pollution monitoring, digital epidemiology, smart grids operations, etc., the structure of the tasks in space or time exhibits a natural linear ordering. Motivated by the above observation, we model the problem of task allocation to strategic crowdworkers as an interval cover mechanism design problem. In this mechanism, a planner (or task requester) needs to crowdsource labels for a set of tasks in a cost effective manner and make a high quality inference. We consider two different scenarios in this problem: homogeneous and heterogeneous, based on the qualities of crowdworkers. We show that the task allocation problem is polynomial time solvable in the homogeneous case while it is NP-hard in the heterogeneous case. When the crowdworkers are strategic about their costs, we design truthful mechanisms for both the scenarios. In particular, for the heterogeneous case, we propose a novel approximation algorithm that is monotone, leading to a truthful interval cover mechanism via appropriate payments.