"I don't want to do my Latin homework." "But I want you to do it." These two simple phrases contain the clues for understanding how the accusative+infinitive construction evolved into indirect statement. The infinitive is nothing more than a verbal noun. In fact, the "-re" ending we are accustomed to seeing at the end of a Latin verb is an ancient dative or locative ending. That meant that the infinitive modified the main verb in an adverbial manner: Possum currere ("I am able to run") originally meant something like "I have ability in the area of running." This kind of expression developed into the Complementary Infinitive.
The infinitive began to be used with other verbs in a different way. A verb such as iubeo took an accusative object - iubeo te - "I order you." The infinitive was added to this construction. For example, volo te scribere, "I want you to write". After a time, the Romans stopped considering te and scribere as two different discrete syntatic units. Instead, the accusative noun and the infinitive began to be thought of as one single construction and attached to verbs of saying, thinking knowing or believing. The birth of the indirect statement!