Product of primary amine and acid anhydride
It should be very clear that a primary amine is a nucleophile and an acid anhydride an electrophile. In the series of carbonyl and carboxyl derivatives, an acid anhydride is classified as quite reactive: more so than aldehydes or ketones, much more than esters or amides but less than acid chlorides. Thus, we should all agree that the first step is the nucleophilic attack on the $\ce{C=O}$ &pi; system via a tetrahedral intermediate to give N-methyl succinic monoamide.


Scheme 1: Mechanism of the monoamide formation.

With that, we can consider whether further reactions will take place. Where we originally had an anime and an acid anhydride, we now have a carboxylate (the $\ce{C=O}$ bond that wasn’t attacked) and a secondary amide. The secondary amide still has a lone pair we might consider to be nucleophilic — but that lone pair is taking part in amide resonance and is thus not available for nucleophilic attack (at least not well). And to remove the amide’s proton, we would need a strong base which we don't have. Thus, the amide side of the equation is far less reactive.

What about the carboxylate? Thus highly symmetric structure is also very unreactive towards nucleophilic attack in the same way as an amide. Due to the negatively charged oxygen donating one of its lone pairs to the &pi; system, the carbon atom is much less electrophilic than in an acid anhydride. Thus, in this case also there is no desire to react.

Since we have two functional groups of low reactivity, the reaction ends here. However, with enough heat (supplying activation energy), it is possible for the sluggish intramolecular reaction between the the amide and the carboxylate to occur. In principle, the mechanism is the same except that you must transfer a few protons and remove water.


Scheme 2: potential onwards reaction to succinimide under harsh conditions.