Question

What is the part of a plot in which the conflicts builds gradually in intensity?

Answer 1

That would be rising action 

Answer 2

Rising action is the part of the plot in which the conflict and the tension increases. During this moment of the plot, interesting events and unexpected revelations occur, increasing a story's stakes. These intense moments eventually erupt during the climax.

The other elements of a plot are: exposition (which happens before the rising action), climax (after the rising action), falling action and resolution.