Let {{MATH_165}} and {{MATH_166}} be defined on a closed interval {{MATH_167}} that contains the value {{MATH_168}}, and let {{MATH_169}} be a constant. The following hold: {{CMD_170}} {{CMD_171}} {{MATH_172}} {{CMD_173}} {{MATH_174}} {{CMD_175}} {{MATH_176}} {{CMD_177}} {{MATH_178}} {{CMD_179}} {{MATH_180}} {{CMD_181}} {{CMD_182}} We will address each property in turn: {{CMD_183}} {{CMD_184}} Here, there is no ``area under the curve'' when the region has no width; hence this definite integral is {{MATH_185}}. {{CMD_186}} This states that total area is the sum of the areas of subregions. Here a picture is worth a thousand words: {{CMD_187}} {{ENV_188}} {{CMD_189}} It is important to note that this still holds true even if {{MATH_190}}. We discuss this in the next point. {{CMD_191}} For now, this property can be viewed as merely a convention to make other properties work well. However, later we will see how this property has a justification all its own.