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Let [math]f[/math] be the step function defined by [math]f(x) = i[/math], if [math]i-1 \lt x \leq i[/math], for every integer [math]i[/math]. Draw the graph of [math]f[/math] and compute the following integrals. (Hint: These problems are neither hard nor long. They require an understanding of the definition of integrability and possibly some ingenuity.

• [math]\int_1^2 f[/math]
• [math]\int_0^3 f[/math]
• [math]\int_{-1}^3 f[/math]
• [math]\int_{-2}^7 f[/math].