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In LaTeX, \int is rendered as inside math mode. To specify the limits (or bounds) of integration, use subscripts and superscripts:

\int_a^b \! f(x) \, \mathrm{d}x.

Note the use of \mathrm to make a Roman "d" which distinguishes it from the product of variables d and x. Note, too, the use of \! to bring the function closer to the integral sign and the \, to push the differential farther away. Without them, the integral looks like

\int_a^b f(x) dx,

which, although logically identical, is less legible and rankles the aesthetic sensibilities of many.

Note: one can also use the \dif command from the commath package to make a Roman "d".


You can also treat the integral as a sum-class symbol with the \limits command. This is most useful for double and triple integrals. For example,

\iint\limits_D \, \mathrm{d} x\,\mathrm{d} y \quad \iiint\limits_E \, \mathrm{d} x\,\mathrm{d} y\,\mathrm{d}z

where D and E are regions that satisfy the requirements.

And let's not forget the closed path integral.

\oint \! \nabla f \, \mathrm{d}t = 0

Note: To obtain double/triple/multiple integrals and cyclic integrals one must use the packages amsmath and esint, respectively.