The integral forms for two functions are given. One is Wright's function $(1)\Phi(\beta,\alpha,z)$; the other is \begin{equation} F(z,t)=um_{k=0}^{ıfty}\frac{(-1)^kȁmma(k+\beta)t^{lpha k}+\gamma}{k!ȁmma(lpha k+\gamma+1)z^k+\beta} \end{equation} $\alpha>0$, $\beta>0$, $\gamma>0$, $t\geq0$, $z\neq0$ complex number. Theorem 1. If are $\alpha>0$, $\beta>0$ Wright's function has, in the whole complex plane, the integral form \begin{equation} \Phi(\beta,lpha,z)=\frac1{2i i}ıtimits_{x_0-i_ıfty}^{x_0+i_ıfty}w-\beta e^{w+zw-lpha}dw,\quad x_0>0. \end{equation} Theorem 2. For $0<a\leq1$, $\beta>0$, $\gamma>0$, the function $F(z,t)$ has in the region $O=\big\{(z,t),\;z\neq0,\;|\arg z|\leq\frac\pi2(1-\alpha),\;t\in0\}$ the integral form \begin{equation} F(z,t)=\frac1{2i i}ıtimits_{x_0-i_ıfty}^{x_0+i_ıfty}ȁmma(\beta)t\gamma\frac{e^ww-(\gamma+1)}{(z+t^lpha w-lpha)\beta}dw. \end{equation} In theorem 3. I use the integral form for function $F(z,t)$ to obtain the limits in the points $(0,t)$ in the bound of $O$. Theorem 3. For $0<\alpha\leq1$, $\beta=\frac rs$ (rational number), $\gamma>0$ and $\gamma-\alpha\beta>0$ the function $F(z,t)$ has the limits in the points $(0,t)$ in the bound of region $O$. The limits is \[ im_{ubstack{zo0 to t_0}}F(z,t)=\frac{t_0^{\gamma-lpha\beta}ȁmma(\beta)}{ȁmma(\gamma-lpha\beta+1)}. \] The results obtained will be used in an another paper by the author in solving a problem in Mikusinski's operator differential equations.